Thiết Kế Bài Giảng Đại Số 10 Nâng Cao Tập 1

"Thiết Kế Bài Giảng Đại Số 10 Nâng Cao Tập 1 🔙 Quay lại trang tải sách pdf ebook Thiết Kế Bài Giảng Đại Số 10 Nâng Cao Tập 1 Ebooks Nhóm Zalo TRAN VINH -2 -1 O NHA XUAT BAN DAI HOG SU PHAM Download Ebook Tai: https://downloadsachmienphi.com Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com TRAN VINH THIET KE BAI GIANG NANG CAO TAP MOT 1 ~' -> NHA XUAT BAN DAI HOC SU PHAM Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Ma sd'; 02.02.80/158.PT 2006 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Ldl NOI DAU Chiiong trinh thay sach gan lien vert viec doi m6i phUdng phap day hoc, trong d6 c6 viec thifc hien ddi mcS phUdng phap day hoc mon Toan. Bo sach Thiet kebai gidng Dqi sd 10 ndng cao va Thiet kebai gidng Hinh hpc 10 nang cao ra dcfi de phuc vu viec ddi mdi do. Bo sach dtfdc bien soan dua tren cac chifdng, muc cua bo sach giao khoa (SGK), bam sat noi dung SGK, txl do hinh thanh nen cau true mot bai giang theo chtfdng trinh mcft dUOc viet theo quan diem boat dong va muc tieu giang day la: L.ay hpc sinh lam trung tam va tich cUc s\i dung cac phifdng tien day hpc hien dai. Phan Dai so gom 2 tap. Tap 1: gom cac chUdng I, chUdng II va chifdng III. Tap 2 : gom cac chifdng IV, chifdng V va chifdng VI. Phan Hinh hpc gom 2 tap: Tap 1: gom chifdng 1, va bai 1 va bai 2 (chifdng II). Tap 2 Phan con lai. Trong moi bai soan, tac gia co difa ra cac cau hoi va tinh huong thu vi. Ve hoat dpng day va hpc, chung toi co gang chia lam 2 phan: Phan boat dpng cua giao vien (GV) va phan boat dpng cua hpc sinh (HS), d m6i phan c6 cac cau hoi chi tiet va hifdng dan tra Icfi. Thifc hien xong moi boat dpng, la da thifc hien xong mot ddn v: kien thifc hoac cung co ddn vi kien thCfc do. Sau moi bai hpc chung toi co dite vao phan cau hoi trac nghiem khach quan nham giup hpc sinh tif danh gia difdc mifc dp nhan thifc va mifc dp tiep thu kien thufc cua minh. Dong thdi, sau m6i bai hpc, chung toi CO gang co nhiing phan bd sung kien thifc danh cho GV va HS kha gioi. Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Phan phu luc la phan danh cho giao vien, nham sif dung cac phan mem cua toan hpc lam chu kien thifc, lam chu cac con so can tinh toan tif do neu len difdc each day mdi chu dpng va sang tao. Day la bp sach hay, difdc tap the tac gia bien soan cong phu, ifng dung mot so' thanh tifu khoa hpc nha't dinh trong tinh toan va day hpc. Chung toi hy vpng dap ifrig difdc nhu cau cua giao vien toan trong viec ddi mdi phifdng phap day hpc. Trong qua trinh bien soan, khong the tranh khoi nhOftng sai sot, mong ban doc cam thong va chia se. Chung toi chan thanh cam dn sif gop y cua cac ban. Tac gia 4 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Chi/dNq I MENH DE - TAP HCfP Ph^n 1. i^imrlirG VAN D £ CUA cm/diiifG I. Npl DUNG Noi dung chinh cua chuong 1 : Menh de : Menh de, phu dinh ciia menh de, menh de keo theo, menh de tuong duong, dinh If va chiing minh dinh li. Tap hop : Khai niem cua tap hop, cac phep toan tren tap hop. Sai so va so g^n diing. Menli die Menh de la mdt khai niem co ban ciia logic toan. Logic toan ciing If thuyet tap hop la co sd ciia moi nganh toan hoc. So gan diing va sai so la nhiing khai niem co ban ciia cac nganh toan irng dung. Cuon sach nay duoc trinh bay thong nha't theo ngon ngCr mSnh dt va tap hop. Nhu vay, cac noi dung ciia chuong I la ra't co ban va c^n thi6't de hoc sinh (HS) hoc tap tie'p cac chuong sau cua chuong trinh Dai so 10 noi rieng, de hoc tap va ling dung Toan noi chung. Sau day la nhirng ndi dung cu the : 1. Khdi niem menh de N6u len khai niem cua de : La cau phai hoac diing hoac sai. Tfnh cha't CO ban cua menh de : M6i menh de chi hoac diing, ki hi6u la 1, hoac sai, kf hieu la 0. SGK khong trinh bay theo gia tri chan If nhung dua tren cac luat CO ban : - Luat bai trung : M6i menh de phai hoac diing, hoac sai, - Luat phi mau thuSn : Mot m6nh d6 khong the vira diing, vura sai. Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com 2. Cdc phep todn ve logic Chiing ta chi trinh bay cac va'n de co ban sau : Phep phii dinh : Menh de phii dinh ciia menh de P la menh deF Hai menh de nay co tfnh chat trai ngugfc nhau ve gia tri chan If : P diing thi P sai va nguoc lai. Phep keo theo : Menh de P keo theo menh de Q, kf hieu la P => Q, chi sai khi P diing Q sai, va diing trong cac trudng hop con lai. Cac each phat biiu menh de keo theo : Neu P thi Q; P la dieu kien du de CO Q; Q la dieu kien can de co P Phep tuang duang : Menh de P tUdng duong vdi Q, kf kieu P <=> Q, la menh d6 chi sai khi P va Q co gia tri chan If nguoc nhau. Cac each phat bieu menh de tuong duong : P khi va chi khi Q; P la dieu kien cSn va du de co Q. 3. Menh de chiia bie'n. Menh de chiia bien chi la menh d6 trong tiing bien cu the hoac ta gSn vao no nhirng ludng tii vdi moi (V) hoac ton tai ( 3). Tap hop /. Khdi niem Tap hop la khai niem khong duoc dinh nghia ma duoc xay dung bang each mo ta thong qua cac phSn tii cua nd. De bieu diin phan tu a thuoc tap hgfp A kf hieu la a e A, phan tii b khong thuoc tap hop A kf hieu b ^ A. Tap hop khong cd phan tu nao goi la tap rdng, kf hieu 0 . Cd hai each cho tap hop : Liet ke cac phan tu cua tap hop hoac rnd ta bang tfnh chat cac phan tu. Tap con : Tap A la tap con ciia tap B, kf hieu A c B, ne'u VxeA thi xeB. 2. Cdc phep todn Chiing ta se hoc cac phep toan sau : Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Phep hop : x e A u B c^ xeA xeB \x&A Phep giao : x e A n B <=> <^ .... . f X e A Phep tru: xe A\ Bc^ \x€B 3. Cdc tap hqp sd Chiing ta se hoc cac tap hop sd : N, Z, Q, R. Ngoai ra chiing ta se gidi thieu ve cac khoang, doan, niia khoang. HsA s o Chiing ta can dat duoc cac don vi kie'n thiic sau : Lam trdn sd gin diing. Sai sd tuyet ddi : Sai sd tuyet ddi cua sd gdn dung a /a A^ = I a - al <^ ddy a Id gid tri gdn diing cua a. Do chfnii xac d : A^< d, ta goi d la do chfnh xac. Sai so tuong ddi : Ti sd -r-j goi la sai sd tuong ddi cua so g^n diing a. Viet chuin so gin diing : Khi biet do chfnh xac d thi ta bie't duoc mot sd g^n diing cd cac chir so nao la chCr so chae, chii sd nao la khdng chae va tir dd ta biet duoc each vie't mot sd gan diing cha'p nhan dugc. n. MUC TIEU 1. Kien thurc Nam dugc toan bd kien thiic co ban trong chuong da neu tren, cu the : Hieu khai niem menh de. Hieu y nghia cac phep toan va kf hieu Idgic thudng gap trong cac suy luan toan hgc. Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Biet dugc ca'u triic thudng gap ciia mdt dinh If trong toan hgc. Hieu the nao la dieu kien can, dieu kien du, dieu kien c^n va dii trong cac dinh If toan hgc, the nao la phuong phap chiing minh bang phan chiing. Nam dugc cac kie'n thiic co ban nha't ve tap hgp, md'i quan h6 giiJa cac tap hgp, cac phep toan tren tap hgp (phep hgp, phep giao, phep la'y hieu va phep la'y ph^n bii). • Nam dugc cac khai niem sai sd tuyet ddi, sai sd tuong ddi, so quy tron, chit so chac. 2. KT nang Bie't diing ngdn ngii va kf hieu ciia If thuye't tap hgp de di6n dat cac bai toan, trinh bay cac suy luan toan hgc mdt each sang siia, mach lac. Bie't tim giao, hgp, lay phan bii ciia cac tap con ciia tap sd thuc thudng gap nhu khoang, doan, nita khoang vd ban. Dilu nay ra't cin thie't cho viec tie'p thu cac chuong tie'p theo ve phuong trinh va he phuong trinh. •Bi6't quy trdn so, xac dinh chir sd chac, va bie't each vie't chuan sd gin diing. Cac kie'n thiic nay cd y nghia thuc ti6n quan trgng. 3. Thai do "Tu giac, tich cue, dgc lap va chii ddng phat hien ciing nhu linh hdi kie'n thiic trong qua trinh hoat ddng. Cin than chfnh xac trong lap luan va tfnh toan. Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Pha n a. CAC BAI SOAIV §1. Menh de va menh de chv^a bien (tiet 1, 2) I. MUC TIEU 1. Kien thurc HS nam dugc : Khai niem menh de. Phan biet dugc cau ndi thdng thudng va menh d6. Khai niem menh de phii dinh, HS can hieu va la'y dugc vf du ve menh de phu dinh. • Khai niem menh di keo theo, HS cin hieu va la'y dugc vf du ve menh de keo theo. Khai niem menh de tuong duong, md'i quan he giira menh de tuong duong va menh de keo theo. Khai niem menh de chiia bien, phan biet dugc menh d6 chiia bie'n va menh de. Bie't sii dung cac kf hieU V va 3 trong viec phat bieu menh di. Biet neu dugc menh de phii dinh ciia mdt menh d6, tii dd xac dinh dugc tfnh diing sai cua mdt menh di. Biet dugc cau triic co ban cua mdt dinh If, dieu kien can, dieu kien dii, dieu kien cin va du. 2. KT nang Sau khi hgc xong bai nay HS phai di6n ta dugc cac bai toan Idgic thdng qua cac kf hieu. Bie't trinh bay Idi giai mdt bai toan, phat bieu mdt dinh If, mdt khai niem toan hgc cd chiia cac khai niem co ban cua menh de. Giai dugc cac bai toan co ban ve menh di, biet chiing minh mdt sd dinh If bang phuong phap phan chiing. • Bie't sii dung cac kf hi6u 3, V trong diln dat menh di Idgic. Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com 3. Thai do Tu giac, tfch cue trong hgc tap. Biet phan biet rd cac khai niem co ban va van trong tirng trudng hgp cu the. Tu duy cac van de ciia toan hpc mdt each Idgic va he thdng. II. CHUAN BI CUA GV VA HS 1. Chuan bi ciia GV De dat cau hdi cho HS, trong qua trinh thao tac day hgc GV cd the chuan bi mot sd kien thiic ma HS da hgc d ldp 9 chang ban : Dau hieu chia het cho 2, cho 3, cho 4, cho 5,...; dau hieu nhan biet tam giac can, tam giac deu,... Chuan bi phan mau, va mdt sd cdng cu khac. 2. Chuan bi cua HS Can dn lai mdt sd kien thiic da hgc d ldp dudi. IIL PHAN PHOI THC)I LUONG Bai nay chia lam 2 tiet : Tiet 1 : Tit ddu den het muc 4. Tie't con Iqi: Td miic 5 den hit vd hudng ddn gidi bdi tap. IV TIEN TRINH DAY HOC A. Dat van de Cau hoi 1 Xet tfnh diing - sai ciia cac cau sau day : a) Mdt sd nguyen cd ba chir sd ludn nhd hon 1000. b) Mdt diem tren mat phang bao gid ciing nam tren mdt dudng thang cho trudc. GV : Nhitng khang dinh cd hai khd ndng : hoac diing hoac sai, ta ndi dd Id nhitng cdu cd tinh diing - sai. Cau hoi 2 Nhiing cau sau day cau nao khdng cd tfnh diing sai? a) 3 la sd nguyen td. 10 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com b) Thanh phd Ha Ndi ra't dep. c)x^-l >0. GV : Ta thdy a) Cd tinh dung - sai. b) Ddy Id cdu cam thdn. c) cd the diing vd cd the sai. Nhitng cdu nhu dqng b) vd c) Id nhitng cdu khdng cd tinh diing sai. Trong ddi sdng hdng ngdy cimg nhu trong todn hgc, ta thudng gap nhiing cdu nhu tren. Nhitng cdu cd tinh diing sai ta ndi dd Id nhiing menh de. B. Bai mdi HOAT DONG 1 1. Menh de la gi? GV: Hudng ddn HS ldm vi du 1, thao tdc hoqt ddng trong 3 phiU. Hoat dong cua GV Cau hoi I Cau a) la cau khang dinh, phu dinh hay nghi va'n? GV: gpi ba HS trd Idi Cau hoi 2 Cau a) la cau khang dinh diing hay sai? GV : Ggi 2 HS trd Idi. Cau hoi 3 cau b) la cau khang dinh, phu dinh hay nghi van? Hoat dong cua HS Ggi y tra Idi cau hoi 1 HS cd the tra Idi ca ba phuofng an : Cau a) la cau khang dinh. cau a) la cau phii dinh. cau a) la cau nghi van. Ddp Cau a) la cau khang dinh. Ggi y tra Idi cau hdi 2 HS cd the tra Idi ca hai phuofng an : Cau a) la cau khang dinh diing. Cau a) la cau khang dinh sai. Ddp cau a) la cau khang dinh diing. Ggi y tra Idi cau hoi 3 HS cd the tra ca ba phuang an : cau b) la cau khang dinh. 11 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Cau b) la cau phu dinh. GV: Ggi 3 HS trd Idi. Cau hoi 4 Cau b) la cau khang dinh diing hay sai? GV: Goi 2 HS trd led. GV: Ddt van de tuang tu ddi vdi cdc cdu c) vd d) Cau b) la cau nghi van. Ggi y tra Idi cau hoi 4 HS cd the tra Idi ca hai phuang an : Cau b) la cau khang dinh diing. Cau b) la cau khang dinh sai. Ddp Cau b) la cau khing dinh sai. Ddp Cau c) la cau khang dinh diing. Cau d) la cau khang dinh sai. GV: Ggi mot vdi HS trd Idi cdc cdu hdi sau HI. Hay neu khai niem menh de. H2. Hay phat bieu the nao la menh de diing. H3. Hay phat bieu the nao la menh de sai. Sau dd GV neu dinh nghia sau : Mdt menh de la mdt cau khang dinh diing hoac mdt cau khang dinh sai. Mdt cau khang dinh diing ggi la mdt menh d6 diing. Mdt cau khang dinh sai ggi la mdt menh de sai. cau khdng phai la cau khang dinh hoac cau khing dinh ma khdng cd tfnh diing - sai thi khdng phai la menh de. HOAT DONG 2 2. Menh de phii dinh GV: Hudng ddn HS ldm vi du 2, thao tdc hoqt ddng ndy trong 3 phiit (3') Hoat ddng cua GV Cau hdi 1 Gia sir cau cua Binh : "2003 la sd nguyen to". 12 Hoat dong cua HS Ggi y tra Idi cau hdi 1 HS cd the tra Idi ca hai phuang an. * Cau cua An la cau khang dinh Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com la cau khing dinh diing. Hdi cau khing dinh ciia An diing hay sai? GV: Goi 2 HS trd Idi. Cau hoi 2 Gia sii cau cua Binh : "2003 la sd nguyen td" la cau khing dinh sai. Hdi cau khing dinh ciia An diing hay sai? GV: Goi 2 HS trd Idi. dung. * cau ciia An la cau khing dinh sai. Ddp: cau ciia Binh diing thi cua An la cau khing dinh sai. Ggi y tra Idi cau hoi 2 HS cd the tra Idi ca hai phuang an. * cau ciia An la cau khing dinh diing. * cau ciia An la cau khing dinh sai. Ddp Cau ciia Binh sai thi cau ciia An la cau khing dinh diing. Neu ki hieu P la menh de ma Binh neu thi menh dd cua An cd the didn dat la "Khdng phai P" va dugc ggi la menh de phu dinh ciia P. GV: Ggi mdt vdi HS phdt bieu HI. The nao la menh de phii dinh ciia menh di P? H2. Neu P diing thi phii dinh cua P la F diing hay sai? H3. Ne'u P sai thi phu dinh ciia P la F diing hay sai? Sau dd neu dinh nghia Cho menh de P. Menh di "Khdng phai P" dugc goi la menh de phu dinh ciia P va kf hieu laF Menh de P va menh de phii dinh P la hai cau khing dinh trai ngugc nhau. Neu P diing thi P sai, ne'u P sai thi P diing. GV: Hudng ddn HS trd Idi \Hl\ vd thao tdc hoqt ddng ndy trong 3 phiU. Hoat dong cua GV Cau hoi 1 Neu menh de phii dinh ciia menh d^ sau va xac dinh xem Hoat dong cua HS Ggi y tra Idi cau hdi 1 *Menh dd phii dinh cua menh de tren la : "Pa-ri khdng phai la thu 13 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com menh de phii dinh do diing hay sai. ' a) Pa-ri la thii dd cua nudc Anh GV: Ggi hai HS trd Idi. Cau hoi 2 Neu menh di phii dinh cua menh de sau va xac dinh xem menh dd phii dinh dd diing hay sai b) 2002 chia he't cho 4. GV: Ggi hai HS trd Idi. do ciia nudc Anh" * Day la mdt menh de diing Ggi y tra Idi cau hdi 2 * Menh de phu dinh cua menh de tren la : "2002 khdng chia he't cho 4" * Menh de phii dinh cua menh di tren la menh d6 diing. HOAT DONG 3 3. Menh de keo theo GV: Neu vd trinh bdy vi du 3, sau dd ddn dat HS di den menh de keo theo • GV thao tdc hoqt ddng ndy trong 3 phiit. Cho hai menh de P va Q. Menh de cd dang "Neu P thi Q" dugc ggi la metih de keo theo va kf hieu la P =^ Q. Hoat ddng cua GV Cau hdi 1 Cho menh de P : "Tam giac ABC cd hai canh bang nhau" Hay phat bieu menh dd Q de menh de P => Q la menh d6 diing. GV: Ggi hai HS trd Idi. Cau hdi 2 Cho menh di A : "a la mdt so 14 Hoat ddng cua HS Ggi y tra Idi cau hoi 1 HS cd the tra Idi nhidu phuang an. Trd led * Menh de Q : "Tam giac ABC can" * Menh de P ^> Q : "Ne'u tam giac ABC cd hai canh bang nhau thi tam giac ABC la tam giac can. Ggi y tra Idi cau hdi 2 Cd rat nhidu phuang an. Sau day la mdt phuang an diing. Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com chan" Hay phat bieu menh de B de menh dS A => B la menh de sai. GV: Ggi hai HS trd Idi. Trd Idi B : "a chia he't cho 3" GV: Hudng ddn HS trd Idi \H2\ vd thao tdc hoqt ddng ndy trong 3 plmt. Hoat ddng cua GV Cau hdi 1 Hay tra Idi cau hdi ciia H2 . GV: Ggi hai HS trd Idi cdu hdi I Cau hdi 2 Hay phat bieu menh de Q ^ P GV: Ggi hai HS trd Idi cdu hoi 2. Cau hdi 3 Trong cac menh dd P => Q va Q => P, menh dd nao diing, menh de nao sai? Hoat ddng cua HS Ggi y tra Idi cau hdi 1 HS cd the tra Idi nhi6u phuang an. Ddp * "Neu tii giac ABCD la hinh chir nhat thi tii giac ABCD cd hai dudng cheo bang nhau" Ggi y tra Idi cau hoi 2 HS cd the tra Idi theo 2 phuang an. Ddp "Ne'u tii giac ABCD cd hai dudng cheo bang nhau thi tii giac ABCD la hinh chir nhat" Ggi y tra Idi cau hdi 3 HS cd the tra Idi nhidu phuang an. Ddp P =^ Q la menh de diing, Q => P la menh de sai. Menh de P ^> Q chi sai khi P diing va Q sai. Ta thudng gap cac tinh hudng sau : • Ca hai menh de P va Q diu diing. Khi dd P => Q la menh di diing. • Menh de P diing va menh de Q sai. Khi dd P => Q la menh de sai. GV: Neu vi du 4 de minh hoa cho cdc khdng dinh tren vd de ket thiic hoqt ddng ndy, GVcd the yeu cdu HS trd Idi cdc cdu hdi sau ddy HI. Hay neu mdt menh di dang P => Q ma ca P va Q cung diing. 15 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com H2. Hay neu mdt menh di dang P => Q ma ca P va Q ciing sai. H3. Hay neu mdt menh de dang P => Q ma P sai va Q diing. H4. Ca ba menh di tren diing hay sai. GV: Neu dinh nghia menh de dao. Cho menh de keo theo P ^> Q. Menh d6 Q => P dugc ggi la menh de dao ciia menh de P ^> Q. GV: Neu vi du S de minh hoa cho dinh nghia tren. HOAT DONG 4 Menh de tuong duong G\': Neu vd trinh bdy vi du 6, sau dd ddn ddt HS di den menh de tuang duang. GV thuc hien thao tdc hoqt ddng ndy trong 3 phut. Cho hai menh d6 P va Q. Menh de cd dang "P neu va chi ne'u Q" dugc ggi la menh de tuang duang va kf hieu la P <» Q. Hoat dong cua GV Cau hoi 1 Cho menh de P : "so nguyen a chia he't cho 6" menh dd Q : " a vira chia het cho 2 vira chia het cho 3" Hay phat bieu menh de P => Q va menh de Q^>P GV: Ggi hai HS trd Idi. Cau hdi 2 Hay phat bieu menh de P <^ Q GV: Ggi hai HS trd lai. 16 Hoat dong ciia HS Ggi y tra Idi cau hdi 1 HS cd the tra Idi theo nhieu phuang an. Ddp : * Menh de P => Q : "Neu sd nguyen a chia he't cho 6 thi a viia chia he't cho 2 viia chia he't cho 3" * Menh de Q ^ P : "Ne'u a viia chia het cho 2 viia chia he't cho 3 thi so nguyen a chia het cho 6" Ggi y tra Idi cau hdi 2 Cd rat nhieu phuang an. Sau day la mdt phuang an diing. Ddp Menh de P <:^ Q : "So nguyen a chia he't cho 6 khi va chi khi a viia chia het cho 2 viia chia he't cho 3" Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Ddi khi ngudi ta con phat bieu menh de P <» Q la "P khi va chi khi Q" • Menh de P <» Q diing neu ca hai mdnh d^ P va Q ciing diing hoac cung sai. • Menh de P <=> Q diing cd nghia la ca hai menh de keo theo P => Q va Q => P deu diing. GV: Yeu cdu HS trd Idi cdc cdu hdi sau ddy : HI. Hay neu mdt menh de dang P <» Q ma ca P va Q ciing diing. H2. Hay neu mdt menh de dang P <=> Q ma ca P va Q cung sai. H3. Hay neu mdt menh de dang P <=> Q ma P sai va Q diing. H4. Trong ba menh de tren, menh de nao diing, menh de nao sai? GV: Hudng dan HS tra Idi \H3\ va thao tdc hoqt ddng ndy trong 3 phiit. Hoat dong cua GV Hoat dong ciia HS Cau hdi 1 Hay tra Idi cau hdi cua H3 a) GV: Goi hai HS trd Idi cdu hdi 1. Cau hoi 2 Hay tra Idi cau hdi ciia H3\b) GV: Goi hai HS trd Idi cdu hdi 2. Ggi y tra Idi cau hoi 1 HS cd thi tra Idi theo nhilu phuang an. Ddp Day la mdt menh de tuang duong. Nd la mdt menh d^ diing. Ggi y tra Idi cau hoi 2 HS cd the tra Idi nhilu phuong an. Trd led Day la loai mdnh de tuong duong va nd la menh de sai. Vi "36 chia he't cho 24" la mdt menh de sai. HOAT DONG 5 5. Khai niem menh de chura bien GV: Trinh bdy theo hudng ddn cua vi du 7 roi ddn ddt HS di den menh de chita bien, sau dd to chicc hoqt ddng trong 3 phiit. 2.TKBGBAISO10NC-T1 17 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Neu kf hieu cau (1) la P(n) thi P(6) la menh de "6 chia he't cho 3" la menh de diing; neu kf hieu cau (2) la Q(x; y) thi Q(l; 2) la menh da "2 > 1 + 3" - dd la menh de sai. Cac cau kieu nhu cau (1) va cau (2) dugc ggi la menh de chda bie'n. Hoat ddng cua GV Cau hdi 1 Hay lay mdt vf du ve menh de chiia bie'n. GV: Ggi 3 HS trd Idi, nen gai y cho HS lay vi du cd ve hinh hgc vd dqi sd. Cau hdi 2 Vdi menh dd chiia bien P(n) va Q(x; y) nhu trdn *P( A = B)l a menh de diing hay sai? * Q(2), Q(3) la cac menh de diing hay menh dd sai? GV: Ggi hai HS trd Idi cdu hdi 2. Hoat ddng cua HS Ggi y tra Idi cau hdi 1 HS cd the tra Idi nhieu phuong an. Cac cau ggi y * P = "Tam giac ABC can" * Q = n^ la mot so chan" Ggi y tra Idi cau hoi 2 HS cd the tra Idi ca hai phuong an : Ddp * P( A = B) la menh de diing. * Q(2) la menh de dung hay menh de sai. * Q(3) la menh dd sai. GV: Hudng ddn HS ldm | H 41. Cd the chia HS thdnh 2 nhdm, mot nhdm xdc dinh P(2), mdt nhdm xdc dinh P(—) sau dd dai dien mSi nhdm trd Idi. 2 Nen thao tdc hoqt ddng ndy trong 3 phiit. Hoat ddng ciia GV Cau hdi 1 (danh cho nhdm 1) Hay xac dinh P(2) va xet xem P(2) la menh dd diing hay menh de sai. 18 Hoat dong ciia HS Ggi y tra Idi cau hoi 1 P(2) : 2 > 2^" pay la menh de sai. Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Cau hoi 2 (danh cho nhdm 2) Hay xac dinh P(—) va xet Ggi y tra Idi cau 1 1 P(^):"i> hoi 2 'if xem P( —) la mdnh de diing hay menh de sai. 2 2 VIJ Day la menh d6 diing. HOATD0NG 6 6. Cac ki hieu V va 3 a) Ki hieu V Cho menh de chiia bien P(x) : "(x - 1) > 0" vdi x la sd thuc. Gan kf hieu V (dgc la "vdi mgi") vao P(x) nhu sau "Vx e E, P(x)" ta dugc cau khing dinh "Ddi vdi mgi sd thuc x thi (x - 1)^ > 0" Day la menh de diing. GV : Hudng ddn HS ldm |H5| trong3phiu. Hoat dong ciia GV Cau hdi 1 (danh cho nhdm 1) n va n + 1 cd th^ la hai sd' ciing le hay khdng? Cau hoi 2 (danh cho nhdm 2) Phat bieu mdnh di "Vn e Z, P(n)" Menh de nay diing hay sai? Hoat dong cua HS Ggi y tra Idi cau hoi 1 Khdng the ciing le vi Ne'u n chan thi n +1 le, neu n le thi n + 1 chan. Ggi y tra Idi cau hoi 2 Menh di "Vdi mgi sd nguydn n, thi n(n + 1) la sd le" la menh d^ sai. 19 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com b) Ki hieu 3 Cho menh de chiia bie'n P(n) : "2" + 1 chia he't cho n" vdi n la sd tu nhien. Gin kf hieu 3 (dgc la "ton tai") vao P(n) nhu sau "3n e N, P(n)" ta dugc cau khing dinh "Tdn tai mdt so tu nhien n de 2" + 1 chia he't cho n" Menh de nay diing, vi ching ban khi n = 3thi2 +1= 9 chia bet cho 3. GV : Hudng ddn HS ldm |H6| trong 3 phiit Hoat ddng ciia GV Cau hoi 1 (danh cho nhdm 1) The nao la sd nguyen to? Cau hoi 2 (danh cho nhdm 2) Phat bi^u menh di "3n e N* Q(n)" Menh de nay diing hay sai? Hoat dong cua HS Ggi y tra Idi cau hoi 1 So nguyen duong ldn hon 1 chi chia he't cho 1 va chinh nd ggi la so nguyen to. Ggi y tra Idi cau hoi 2 Menh de "Tdn tai sd nguyen duong n de 2" - 1 la so nguyen td" la menh de diing, vi vdi n = 5 thi 2 - 1 = 31 la so nguyen td'. HOAT DONG 7 7. Menh de phii dinh cua menh de co chiia ki hieu V, 3 GV : Trinh bdy theo hudng ddn cua vi du 10,11 rdi ddn dat HS di de'n menh de phii dinh ciia menh de cd chda ki hieu V vd 3, sau dd to chitc hoqt ddng |H7| trong 3' • Cho menh de chiia bie'n P(x) vdi x e X. Menh de phii dinh cua menh de "Vx e X, P(x)" la "3x e X, P(x) 20 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com • Cho menh de chiia bie'n P(x) vdi x G X. Menh de phii dinh ciia menh de "3x e X, P(x)" la "Vx e X, P(x)" Hoat ddng ciia GV Cau hoi 1 (danh cho nhdm 1) Phat bieu menh de tren bang each sir dung cac kf hieu 3 va V Cau hoi 2 (danh cho nhdm 2) Phat bieu inenh de phu dinh ciia mdnh d^ tren. Hoat dong cua HS Ggi y tra Idi cau hoi 1 V HS trong ldp ddu cd may tfnh. Ggi y tra Idi cau hoi 2 3 mdt ban HS ldp em khdng cd may tfnh. 21 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com TOM TA T BAI HOC 1. Mdt menh de la mdt cau khing dinh diing hoac mdt cau khing dinh sai. Mdt cau khing dinh diing ggi la mdt menh de diing. Mdt cau khing dinh sai ggi la mdt menh d^ sai. 2. Cho menh de P. Menh di "Khdng phai P" dugc ggi la menh de phii dinh ciia P va kf hieu laF Menh de P va menh de phu dinh P la hai cau khing dinh trai ngugc nhau. Ne'u P diing thi P sai, ne'u P sai thi P dung. 3. Cho hai menh d6 P va Q. Menh de cd dang "Ne'u P thi Q" dugc ggi la menh de keo theo va kf hieu la P => Q. 4. Cho hai menh de P va Q. Menh de cd dang "P ne'u va chi neu Q" dugc ggi la menh di tuong duong va kf hieu la P <=> Q. 5. Khai niem nienh di chiia bie'n. 6. Cho menh de chiia bie'n P(x) vdi x e X. Menh da phii dinh ciia manh de "Vx e X, P(x)" la "3x e X, P(x)" Cho menh da chiia bien P(x) vdi x e X. ^4anh de phu dinh cua manh de "3x e X, P(x)" la "Vx G X, P(x)" ^^ MOT SO CAU HOI TRAC NGHIEM ON TAP BAI 1 1. Hay xet tfnh diing sai ciia cac menh de sau bang each danh da'u x vao 6 vudng thich hgp sau day : (a) Thanh Hoa la mdt tinh thudc Viet Nam. Diing [j Sai[j; (b) 99 la sd nguyan to Diing LI Sai [J; (c) 1025 la sd chia het cho 5 Diing 0 SaiQ; (d) 45 la sd hCru ti Diing [] Sai Q • 22 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com 2. Cho menh da 4l2 la mdt sd vd ti" Hay chgn menh da phii dinh cua menh de tran trong cac menh de sau day : (a) 4l2 la hgp sd; (b) Vl2 la sd nguyan to; (c) 4\2 la sdhuu ti; (d) 4l2 = 3. 3. Hay xet tfnh diing sai ciia cac menh de sau bang each danh da'u x vao d vudng thfch hgp sau day : (a) Na'u a la so nguyan to thi a la so nguyan td; Diing [j Sai[j; (b) Na'u 12 la sd nguyen td thi khdng cd su sdng trong mat trdi; Diing D SaiD; (c) Na'u 12 la hgp sd thi 15 la sd nguyan to; Diing [J Sai[j; (d) Na'u 12 la hgp so thi 2 la sd nguyan td; Diing [j SaiLJ. 4. Hay xet tfnh diing sai ciia cac menh da sau bang each danh da'u x vao d vudng thfch hgp sau day : (a) X = a <=>x = 4a Diing [j Sai [J; (b) a chia he't cho 4 khi va chi khi a chia ba't cho 2. Diing D SaiD; (c) a khdng phai la sd nguyan td khi va chi khi a la hgp sd. Diing n SaiD; (d) a chia ba't cho 2 khi va chi khi a cd chir sd tan ciing la sd chan. 5. Hay xet tfnh diing sai ciia cac menh de sau bang each danh dau x vao d vudng thfch hgp sau day : (a)x>2<^x'^ >4 DiingD Sai^ ; (b)00<=>12>4 DiingD SaiQ 6. Cho menh de P : "2n + 3 la mdt sd nguyan chi ba't cho 3" Hay xet tfnh diing sai cua cac menh de sau bang each danh da'u x vao d vudng thfch hgp sau day : (a)P(3) DiingD SaiQ: (b)P(4) Diing n SaiD; (c)P(5) DiingD SaiD; (d)P(6) DiingD SaiD 7. Menh de phii dinh ciia menh d^ P : ' x + x + 1 > 0" vdi mgi x la. (a) Ton tai x sao cho x + x + 1 > 0; 'y (b) Tdn tai x sao cho x + x + 1 < 0; (c) Ton tai x sao cho x + x + 1 = 0; (d) Ton tai x sao cho x + 1 > 0. 8. Menh de phu dinh ciia menh de P : ' 3 x : x + x + 1 la so nguyan i6" Menh de phu dinh ciia menh de P la : 2 (a) V X : X + X + 1 la sd nguyan td" 2 (b) 3 X : X + X + 1 khdng la so nguyan to" (c) V X : x^ + X + 1 la hgp sd" (d) 3 X : x^ + X + 1 la sd thuc'' 9. Hay xet tfnh diing sai cua cac menh de sau bang each danh da'u x vao 6 vudng thich hgp sau day : (a) V X G N : x^ + X + 1 la sd nguyan to" DiingD Sai D (b) 3x G N: x^ + x +1 lahgpsd" DiingD SaiD 24 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com (c) " V X G N : x^ + X + 1 la hgp so" DiingD Sai D (d) 3xG N : x^ + x+ 1 lasdthuc" DiingD SaiD 10. Cho menh de P : " Sd nguyan td la sd le" Menh de dao cua menh de P la menh de : (a) Sd le la sd nguyen td; (b) Sd le la hgp sd; (c) So le chia he't cho 1 va chfnh nd la sd nguyan td; (d) Ton tai sd le khdng la so nguyan td. Dap an: l.(a)D 2.(c) 3. (a) S 4. (a) S 5. (a) S 6. (a)D^ 7.(b) 8.(b) 9. (a) S 10. (d). (b)S (b)D (b)S (b)D (b)S (b)D (c)D (c)D (c)S (c)D (c)S (c)S (d)S (d)S (d)D (d)D (d)D (d)D 25 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com HUdNG DAN BAI TAP SACH GIAO KHOA Bai 1. GV: Hitdng ddn hgc sinh ldm bdi tap ndy a nhd. Cau hdi Cau hdi 1 Cau "Hay di nhanh len" cd phai menh di hay khdng? Cau hdi 2 Khing dinh : 5 + 7 + 4 = 15 Co phai menh di hay khdng? na'u la menh de thi la menh d^ diing hay menh di sai? Cau hdi 3 cau hdi tuong tu ddi vdi cau "Nam 2002 la nam nhuan" Bai 2. Ggi y tra Idi Ggi y tra Idi cau hoi 1 Day la cau menh lenh, khdng cd tfnh diing - sai. Khdng phai mdnh di. Ggi y tra Idi cau hoi 2 Day la khing dinh sai, do dd nd la mdt menh da sai. Ggi y tra Idi cau hoi 3 - Nam a la nam nhuan na'u a chia het cho 4. cau tran la mdt khing dinh sai, do do nd la manh de sai. GV: Hudng ddn hgc sinh ldm bdi tap ndy a nhd. De ldm bdi tap ndy, HS can dgc kl Iqi khdi niem menh de phu dinh, gid tri chdn li cua menh de phii dinh; xem Iqi cdc vi du 2 vd H\\. Trd Idi cdc cdu hdi sau ddy. Cau hdi Cau hdi 1 Cho phuong trinh : x^ - 3x + 2 = 0, hay tfnh A va ke't luan ve nghiem cua phuong trinh. 26 Ggi y tra Idi Ggi y tra Idi cau hoi 1 A = 1 > 0. Phuong trinh cd hai nghiem. Tron Bo SGK: htts://bookiaokhoa.com Cau hdi 2 Download Ebook Tai: https://downloadsachmienphi.com Ggi y tra Idi cau hdi 2 Nau menh de phu dinh cua menh de "Phuang trinh x^ - 3x + 2 = 0 cd nghiem" va xet tfnh diing - sai cua menh de phii dinh. Cau hoi 3 - Neu menh de phu dinh ciia menh da P : "2^° - 1 chia he't cho 11" - Xet tfnh diing sai ciia P vaP Cau hoi 4. - Neu menh de phii dinh Q cua menh di Q : "Cd vd so so nguyen to'" - Xet tinh diing sai cua Q va Q. Bai 3. "Phuang trinh x^ - 3x + 2 = 0 vd nghiem" Day la menh de sai vi menh da : "Phuang trinh x^ - 3x + 2 = 0 cd nghiam" la mdnh da diing. Ggi y tra Idi cau hdi 3 P : "2 - 1 khdng chia he't cho 11" Menh de P la menh de diing. Cd the dimg may tfnh de tfnh 2'"- 1 = 1024 - 1 = 1023 = 11.93. P la menh da sai. Ggi y tra Idi cau hoi 4 Menh de Q : "Cd hihi ban so nguyan td" Day la menh de sai vi menh de Q diing. GV: Hudng ddn hgc sinh ldm bdi tap ndy d nhd. De ldm bdi tap ndy, HS can dgc ki Iqi khdi niem menh de tuang duang, gid tri chdn li ciia menh tuang duang; xem Iqi cdc vi du 6 vd \H3\. Trd Idi cdc cdu hdi sau ddy. Cau hoi cau hoi 1 Hay phat bieu menh d^ P<=>Q. Cau hdi 2 Cho bie't menh dd P => Q diing hay sai? Ggi y tra Idi Ggi y tra Idi cau hoi 1 HSiTir phat bieu. Chii y cd the dimg cac ttr" Khi va chi khi, neu va chi neu, dieu kidn c^n va du" Ggi y tra Idi cau hdi 2 P ^> Q la menh de diing. 27 Tron Bo SGK: htts://bookiaokhoa.com Cau hoi 3 Download Ebook Tai: https://downloadsachmienphi.com Ggi y tra Idi cau hdi 3 Cho bie't menh de Q => P diing hay sai? Cau hdi 4. Cho bie't menh de P <=> Q diing hay sai? Bai 4. Q => P la menh de diing. Ggi y tra Idi cau hdi 4 P <» Q la menh de diing. De ldm bdi tap ndy, HS edn dgc ki Iqi khdi niem menh de chita bien, xem Iqi cdc vi du 7 vd \H4\. Trd Idi cdc cdu hdi sau ddy. Cau hdi Cau hdi 1 Hay xac dinh P(5). Cau hoi 2 Manh de P(5) diing hay sai? Cau hdi 3 Hay xac dinh menh de P(2). Cau hdi 4. Menh de P(2) diing hay sai? Bai 5. Ggi y tra Idi Ggi y tra Idi cau hdi 1 Manh de P(5) : P(5) : "5^ - 1 chia ha't cho 4" Ggi y tra Idi cau hoi 2 Vi 25 - 1 = 24 chia he't cho 4 nan P(5) la menh de diing. Ggi y tra Idi cau hdi 3 Menh de P(2) : P(2) : "2^ - 1 chia het cho 4" Ggi y tra Idi cau hdi 4 Vi 4 - 1 = 3 khdng chia he't cho 4, nan menh de P(2) la menh de sai. De gidi bdi tap ndy, HS can dgc ki khdi niem menh de chita bien cd gdn cdc ki hieu B vd V. Cdc menh de phu dinh cua chiing; xem Iqi vi du 8, vi du 9, \H5\ vd\H6\. HS trd Idi cdc cdu hdi sau ddy : 28 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Cau hdi Cau hdi 1 - Hay chi ra mdt so n ma n^ - Ikhdng la bdi cua 3. - Neu menh di phii dinh ciia menh da "Vn G N* n^ - 1 la bdi so ciia 3" Cau hdi 2 Neu menh de phu dinh ciia menh de sau : Vx G M, x^ - X + 1 > 0; Cau hoi 3 Nau menh da phii dinh cua menh de sau : "3 X G Q, x^ = 3" Cau hdi 4 Nau menh de phii dinh ciia menh di "3n G N, 2" + 1 la sd nguyen td" Cau hoi 5 Neu menh di phii dinh ciia menh d^ : "Vn G N, 2" > n + 2" Ggi y tra Idi Ggi y tra Idi cau hdi 1 n = 3, 6,... Menh da phu dinh : * 2 "3 n G N n- 1 khdng chia he't cho 3" Day la menh di diing. Ggi y tra Idi cau hdi 2 Menh de phu dinh "3xG R, x^ -x + 1 <0 " Day la menh da sai. Ggi y tra Idi c^u hoi 3 Menh de phu dinh la "Vx G Q, x^^3" Ggi y tra Idi cau hdi 4 Menh da phu dinh "Vn G N, 2" + lla hgp so" Ggi y tra Idi cau hdi 5 Menh de phu dmh "3n G N, 2" < n + 2" 29 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com BO SUNG KIEN THLfC 1. Bang chan li Ngudi ta quy udc mdt menh de diing cd gia tri chan If bang 1, menh de sai cd gia tri chan If bang 0. Ta cd bang chan tri sau p 1 1 0 0 Q 1 0 1 0 P=>Q 1 0 1 1 P 1 1 0 0 Q 1 0 1 0 P » Q 1 0 0 1 Bdng chdn tri cda menh de keo theo Bdng chdn tri cua menh de tuang duang 2. Menh de hoi va menh de tuyen Ngoai cac phep toan phu dinh, keo theo va tuong duong, ta con diing hai phep toan logic khac la phep hoi vd phep tuyen di tao ra menh da mdi tii cac menh de da cd. a) Dinh nghia : Cho hai menh de P va Q. Menh da "P va Q" ggi la hdi cua P va Q, kf hieu la P A Q. Menh de hdi chi diing trong trudng hgp ca P va Q ciing diing. Menh di nay sai trong cac trudng hgp edn lai. Phep toan Idgic A ggi la phep hdi. Menh de "P hoac Q" ggi la tuyen cua P va Q, kf hieu la P v Q. Menh de tuyen chi sai trong trudng hgp ca P va Q deu sai va diing trong cac trudng hgp con lai. Phep toan Idgic v" ggi la phep tuyen. 30 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com b) Bdng chdn li cua cdc menh de hdi vd tuyen nhu sau P 1 1 0 0 Q 1 0 1 0 P A Q 1 0 0 0 P 1 1 ,. 0 0 Q 1 0 1 0 P v Q 1 1 1 0 Bdng chdn tri ciia menh de hoi Bdng chdn tri ciia menh de tuyen c) Cdc phep todn logic hdi vd tuyen cd cdc tinh chdt sau day : Tinh chdt giao hodn P v Q = QvP ; PAQ=QAP . Tinh chdt ke't hap (P V Q) V R = P V (Q V R); (P A Q) A R = P A (Q A R). Tinh chdt phdn phoi giiCa hai phep todn. P V (Q A R) = (P V Q) A (P V R); P A (Q V R) = (P A Q) V (P A R). Quy tdc Dd Mooc-gdng PvQ PAQ=PVQ = P A Q; Mot vdi tinh chdt khdc P:^Q=FV(2 ; P::^Q=Q^ F Trong cac cdng thiic tran da'u '=" giira hai menh de dugc hieu la hai menh de dd cd ciing mdt gia tri chan If. 31 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com §2. Ap dung menh de vao suy luan toan hoc (tiet 3) I. MUC TIEU 1. Kie'n thurc HS nim dugc: Khai niem dinh If, ca'u triic ciia dinh If, chiing minh dinh If. Khai niem dieu kien cin, dieu kien dii, diau kien can va dii. Khai niem dinh If dao ciia mdt dinh If. 2. KT nang Sau khi hgc xong bai nay HS nau dugc gia thie't va ka't luan ciia dinh If, bia't each chiing minh mdt dinh If bang phuong phap phan chiing. Bie't phat bieu mdt dinh If dudi nhieu dang khac nhau. Xac dinh mdt each nhanh chdng dieu kien can, diau kian dii, dieu kien can va du ciia mdt cac menh da chiia bia'n trong mdt dinh If. 3. Thai do Bia't van dung menh da trong suy luan Idgic. DiSn dat cac dinh If, menh de mdt each mach lac, rd rang. n . CHUAN BI CUA GV v A HS 1. Chuan bi cua GV: • De dat cau hdi cho HS, trong qua trinh day hgc GV cin chuin bi mot s6' kien thiic ma HS da hgc d ldp dudi ching ban : - Cac dinh If: ve tam giac ddng dang, ve hinh binh hanh, dudng trdn,... - Da'u hieu nhan biet tam giac can, tam giac deu,... Chuan bi phan mau, va mdt sd cdng cu khac. 32 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com 2. Chuan bi cua HS : • Cin dn lai mdt sd kia'n thiic da hgc d ldp dudi, cac dinh If, cac da'u hieu. ra. PHA N PHd l TH6 I LUONG Bai nay day trong 1 tiet: Phdn kiem tra bdi cU : 5 phiit. Phdn li thuyet: 30 phiit. Hudng ddn gidi bdi tap: 10 phut. IV. TI^N TRINH DAY HOC A. Bai cu Cdu hoi 1 Hay nau menh di phii dinh ciia cac menh d^ sau: 1) V X G R, x S 0. 2) 3 n G N, n^ chia het cho 3. Cau hoi 2 Hay xac dinh tfnh diing - sai ciia cac menh de keo theo sau day: 1) Ne'u mdt tam giac cd ba canh bang nhau thi ba gdc bang nhau. 2) Neu ham y = ax + b cd a > 0 thi ham sd ddng bie'n. B. Bai mdi HOAT DONG 1 1. Dinh li va churng minh dinh li Vidul. Xet dinh li "Ne'u n la sd tu nhien le thi n^ - 1 chia het cho 4" Dinh li nay dugc hi^u mdt each diy dii la "Vdi mgi sd tu nhian n, na'u n la sd le thi n^ - 1 chia ha't cho 4" 3.TKBGOAIS610NC-T1 33 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com GV: Yeu cdu HS trd Idi mot sd cdu hdi sau, HS trd Idi, GV phdn tich vd di den khdi niem dinh li. HI. Hay neu mdt sd dinh If ma em da hgc, nau gia thiet va ket luan cua dinh If. H2. Em da biet dinh If nao sai chua? H3. Hay nau mdt dinh If ma em biet dudi dang menh de keo theo. H4. Hay nau mdt dinh If ma em bia't dudi dang menh da tuong duong. Khai niem: Trong toan hgc, dinh li la nhiing menh de diing. Thdng thudng dinh If dugc phat bieu dudi dang Vx G X, P(x) => Q(x), (1) trong do P(x) va Q(x) la cac menh de chiia bia'n, X la mdt tap hgp nao dd. Chiing minh dinh If (1) cd nghia la diing cac suy luan va cac kie'n thiic da bia't de khang dinh ring menh de (1) la diing. Cd the chiing minh dinh If (1) true tiep hay gian tiep. Phep chifng minh true tie'p gdm cdc budc sau : • Gia thiet rang x G X va menh de P(x) dung. • Diing cac suy luan va cac kie'n thiic toan hgc da biet de chi ra ring menh de Q(x) la diing. GV: Neu vi dii 2 vd hudng ddn HS theo thao tdc sau: Hoat ddng ciia GV Cau hdi 1 Hay neu gia thie't va ke't luan ciia dinh If. Cau hdi 2 Hay nau dang ciia mot so le. Cau hdi 3 Hay phan tich n - 1 thanh nhan tir 34 Hoat ddng ciia HS Ggi y tra Idi cau hdi 1 GT: n la sd tu nhian le. 2 KL: n- 1 chia hat cho 4. Ggi y tra Idi cau hoi 2 Dang cua mdt sd' le : 2k + 1 hoac 2 k - 1, vdik G N. Ggi y tra Idi cau hdi 3 Tii hang ding thiic tren ta cd : Tron Bo SGK: htts://bookiaokhoa.com Cau hdi 4 Download Ebook Tai: https://downloadsachmienphi.com n l = (n-l)(n+l) . Ggi y tra Idi cau hoi 4 Ne'u ta la'y dang ciia so le la : n = 2k + 1, hay thay vao gia thiet va chiing minh dinh If. Tir hang ding thiic tren ta cd : n^-l=(n-l)(n+l) . So le n CO dang n = 2k + 1, k GN . Vayn^-l=4k(k+l) . GV: Neu cdc budc chdng minh dinh li bang phdn chdng : - Gia su ton tai Xy G X sao cho P(X()) diing va Q(x,)) sai. - Dung li luan din den mau thuin. GV: Hudng ddn HS ldm vi du 3 trong 4 phut, theo cdc thao tdc sau. Hoat ddng cua GV Cau hoi 1 Hay ndu gia thie't va ket lualn ciia dirrh li. Cau hdi 2 Gia sii m khdng cit b. Ta cd dieu gi? Cau hdi 3 Ne'u mil b, ta din den diin gi? Cau hoi 4 Cd dieu gi mau thuin vdi gia thiet? ' Hoat ddng ciia HS Ggi y tra Idi cau hdi 1 GT: all b, m cit a. KL: m cit b. Ggi y tra Idi cau hdi 2 m//b . Ggi y tra Idi cau hoi 3 m // a hoac m triing a. Ggi y tra Idi cau hdi 4 GT ndi ring m cit a. GV: Hudng ddn HS /am|H1|. Cd the chia HS thdnh 2 nhdm, mdi nhom dua ra 3 trudng hap cu the cua 3n + 2 sau dd dqi dien mdi nhom trd Idi, vd hudng ddn HS chdng minh dinh li. 35 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Hoat ddng cua GV Cau hdi 1 Neu GT va KL cua dinh li. Cau hdi 2 Hay chiing minh dinh li bing phan chiing. Hoat ddng ciia HS Ggi y tra Idi cau hdi 1 GT : V n G N, sao cho 3n + 2 la sd tu nhien le. KL: n le. Ggi y tra Idi cau hdi 2 Gia sir n la sd chan thi 3n chin va 3n + 2 la sd chan, vd If. HOATDONG 2 2. Dieu kien can, dieu kien du Cho dinh li dang (1) "Vx G X, P(x) => Q(x)" (1) Ngudi ta ggi P(x) la gia thia't va Q(x) la ket luan cua dinh If. Ta edn ndi : P(x) la dieu kien du de cd Q(x) hoac Cling ndi : Q(x) la dieu kien can de cd P(x). Vi du 4. Xet dinh If "Vdi mgi so tu nhian n, neu n chia het cho 24 thi nd chia het cho 8. Khi dd, ta ndi n chia he't cho 24 la dieu kien dii de n chia het cho 8" hoac ciing ndi "n chia het cho 8 la dieu kian cin de n chia he't cho 24" 36 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com GV: thuc hien thao tdc ndy trong 2 phdt. Hoat ddng ciia GV Cau hoi 1 Hay neu mdt dinh li, neu gia thia't va ka't luan cua dinh li dd. Hay phat hiiu dinh If dudi dang di^u kidn cin va dieu kian dii. GV: Hudng ddn HS ldm \H2^ Hoat ddng ciia HS Ggi y tra Idi cau hdi 1 • Na'u a, b la cac so chin thi a + b la so chan. • a, b la cac so chin la dieu kien dii de a + b chin a + b chin la dieu kien cin de a va b chin. Trd Idi: P(n) : n chia het cho 24", Q(n) : "n chia het cho 8" HOATD0NG3 3. Djnh Ii dao, dieu kien can va dii Menh de "Vx G X, Q(x) ^ P(x)" (2) ggi la menh de dao cua menh de (1). Tuy nhian menh de (2) cd the diing, cd the sai. Na'u menh de (2) diing thi nd dugc ggi la mdt dinh li dao. Liic dd dinh If (1) se dugc ggi la dinh li thuan. Dinh If thuan va dao cd the viet gdp thanh mdt dinh If " Vx G X, P(x)« Q(x)" Khi do, ta edn ndi: P(x) la dieu kien can vd du di cd Q(x). GV: Yeu cdu HS trd Idi cdc cdu hoi sau: HI. Cho menh de "Vx G X, Q(x) =^ P(x)" Khi nao menh de tran la mdt dinh If? H2. Na'u menh de tren la dinh If hay phat bieu dinh If dao ciia nd. 37 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com H3. Khi ca dinh If thuan va dinh If dao cung diing. Hay phat bieu gdp hai dinh ll. H4. Hay la'y mdt vf du va dinh If thuan va dinh If dao ma em biet. Ngoai ra ta con ndi "P(x) neu va chi ne'u Q(x)" hoac "P(x) khi va chi khi Q(x)" hoac "Diau kien cin va dii di cd P(x) la cd Q(x)" GV: Hudng ddn HS thuc hien H 3 Hoat ddng ciia GV Cau hdi 1 Dinh li tren via't dudi dang "VneN, P(n)oQ(n) Hay xac dinh P(n) va Q(n). Cau hoi 2. Su dung thuat ngii "dieu kien Hoat ddng cua HS Ggi y tra Idi cau hdi 1 P(n) : n chia he't cho 3. Q(n) : n^chiacho3dul . Ggi y tra Idi cau hoi 2 "Dieu kien cin va dii d^ mdt so he't 38 cin va dii de phat bieu dinh li trdn. nguyen duong n khdng chia cho 3 la n chia cho 3 du 1" Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com TOM TAT BA I HO C 1. Trong toan hgc, dinh If la nhung manh de dung. Thdng thudng dinh If dugc phat bieu dudi dang Vx G X, P(x) =^ Q(x), (1) trong dd P(x) va Q(x) la cac menh de chiia bien, X la mdt tap hgp nao dd. 2. Phep chirng minh true tiep gom cac budc sau : • Gia thiet ring x G X va menh da P(x) diing. • Diing cac suy luan va cac kien thiic toan hgc da bia't de chi ra ring menh de Q(x) la diing. 3. Phep chiing minh bing phan chiing - Gia sii ton tai x,, G X sao cho P(X(,) diing va Q(X()) sai. - Diing If luan din da'n mau thuin. 4. Menh di "Vx G X, Q(x) => P(x)" (2) ggi la menh de dao ciia menh de (1). Tuy nhian menh da (2) cd the diing, cd the sai. Na'u menh di (2) dung thi nd dugc ggi la mdt dinh If dao. Liic do dinh If (1) se dugc ggi la dinh If thuan. Dinh If thuan va dao cd the via't gdp thanh mdt dinh If " V,Y G X, P(x) o Q(x) " 39 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com M OT sd cAu HOI TRAC NGHI$M 1. Xet dinh If: "Trong mdt tam giac, tong ba gdc bing 180°" Hay chgn ket qua diing trong cac ka't qua sau: (a) "Tong ba gdc bing 180°" la dieu kien can de cd "mdt tam giac" (b) "T6ng ba gdc bing 180°" la dieu kien du de cd "mdt tam giac" (c) "Mdt tam giac'' la dieu kian cin de cd "tong ba gdc bing 180°" (d) Ca ba khing dinh tren deu sai. 2. Xet dinh If: "n chia het cho 5 khi va chi khi n chia het cho 5" Phep chiing minh dinh li bit diu sai tCf budc nao? (a) Budc 1. Gia sii n chi het cho 5 edn n khdng chia het cho 5. (b) Budc 2. Khiddn^ = n. n (c) Budc 3. n^ = (5k + l)(5k + 1) = 25k^ + 10k + 1. 2 2 (d) Budc 4. Do 25k ; 10k chia het cho 5; 1 khdng chia ha't cho 5 nan n khdng chia het cho 5. Trai vdi gia thiet. 3. Xet dinh If: "Trong mdt tam giac can, hai dudng cao tuong iing vdi hai canh ban bing nhau" Trong cac dinh If sau day, dinh If nao la dinh If dao? (a) Trong mdt tam giac can, hai dudng phan giac cua hai gdc day bing nhau. (b) Trong mdt tam giac can, hai dudng cao xua't phat tur dinh vudng gdc vdi day. (c) Tam giac cd hai dudng cao tuong iing vdi hai canh ben bing nhau la mdt tam giac can. 40 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com (d) Tam giac cd hai dudng trung tuyen tuong iing vdi hai canh ban bing nhau la mdt tam giac can. Ddp dn: 1. (a) 2. Sai tii budc 3 do thia'u cac trudng hgp khac. 3. (c). HU6NG DA N GIA I BA I TAP SGK Bai 6. D^ giai bai tap nay, HS can: - Dgc kl If thuyet phan dinh If, dinh If thuan va dinh If dao. -XemlaiVfdu l,Vfdu2. GV: Hudng ddn HS theo cdc cdu hoi hoqt ddng sau: Cau hdi Cau hdi 1 Hay phat bieu menh de dao cua menh di tren. Cau hdi 2. Menh de dao diing hay sai? Bai 7. De giai bai tap nay, HS cin: Ggi y tra Idi Ggi y tra Idi cau hdi 1 Ne'u tam giac cd hai dudng cao bing nhau thi tam giac dd can Ggi y tra Idi cau hdi 2 Menh da dao diing. - Dgc kl If thuya't, cac budc chiing minh bing phan chiing. Xem lai Vf du 3 va H 1 41 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com GV: Hitdng ddn HS theo cdc cdu hdi hoqt ddng sau: Cau hdi Cau hdi 1 Hay ndu budc 1, de chiing minh bing phan chiing dinh K tren Cau hdi 2. Hay di tim mau thuin. Bai 8. De giai bai tap nay,'HS cin: - Dgc kl If thuyet, xem ki muc 2. Xem lai Vf du 4 va H2 Ggi y tra Idi Ggi y tra Idi cau hdi 1 Gia s\xa + b<24ab vdi a, b la hai sd khdng am. Ggi y tra Idi cau hdi 2 a + h-24ab =(4a-4b)^ <0,vdU. GV: Hudng ddn HS theo cdc cdu hdi hoqt ddng sau: Cau hdi Ggi y tra Idi Cau hdi 1 Ne'u dinh If phat bieu dudi dang P :^> Q. Hay tim P va Q. Cau hdi 2. Md'i quan he giira P va Q trong dinh If tren. Trd led: Ggi y tra Idi cau hdi 1 P : a va b la hai so hiiu ti. Q: a + b la so hiiu ti. Ggi y tra Idi cau hdi 2 Q la diau kien can de cd P P la dieu kien dii de cd Q. Dieu kien dii de tong a + b la so hiiu ti la ca hai so a va b deu la so hiiu ti. Bai 9. De giai bai tap nay, HS cin: 42 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Dgc kl If thuyet, xem ki muc 2. - Xem lai Vi du 4 va H2 GV: Hudng dan HS theo cdc cdu hdi hoqt ddng sau: Cau hdi Cau hdi 1 Na'u dinh li phat bieu dudi dang P => Q. Hay tim P va Q. Cau hdi 2. Mdi quan he giiia P va Q trong dinh li tren. Trd Idi: Ggi y tra Idi Ggi y tra Idi cau hdi 1 P : a la so tu nhien chia he't cho 15 Q: a chia het cho 5. Ggi y tra Idi cau hoi 2 Q la dieu kien cin de cd P P la dieu kien dii de cd Q. Dilu kien cin de mot sd chia he't cho 15 la nd chia he't cho 5. Bai 10. De giai bai tap nay, can - Dgc kl If thuyet, xem kT muc 3. - Xem lai //3 GV: Hudng ddn HS theo cdc cdu hdi hoqt ddng sau: Cau hoi Cau hdi 1 Na'u dinh li phat bieu dudi dang P ^> Q. Hay tim P va Q. Cau hdi 2. Md'i quan he giiia P va Q trong dinh If tren. Ggi y tra Idi Ggi y tra Idi cau hdi 1 P : Tii giac ndi tiep trong dudng trdn. Q: Tong hai gdc ddi bing 180° Ggi y tra Idi cau hdi 2 Q la diau kien can de cd P P la diau kien du de cd Q. 43 Tron Bo SGK: htts://bookiaokhoa.com Trd Idi: Dieu bing 180° Download Ebook Tai: https://downloadsachmienphi.com kien cin va du d^ mdt tii giac ndi tie'p la tdng hai gdc ddi Bai 11. De giai bai tap nay, cin - Dgc kl ll thuya't, xem ki muc 1. - Xem lai vf du 3 va HI GV: Hudng ddn HS theo cdc cdu hdi hoqt ddng sau: Cau hoi Ggi y tra Idi Cau hdi 1 Hay neu budc 1, de chiing minh bing phan chiing dinh K tren Cau hoi 2. Hay tim ra mau thuin 44 Ggi y tra Idi cau hdi 1 Gia sii n chi he't cho 5 con n khdng chia he't cho 5. Ggi y tra Idi cau hdi 2 n cd chii sd' tan ciing khac 0 hoac khac 5. Do dd n cd chii so tan 2 ciing khac 0 hoac khac 5 hay n khdng chia het cho 5 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com . -^^ Luyen tap (tiet 4) I. MUC TifiU 1. Kie'n thiirc Thdng qua bai tap luyen tap dn tap toan bd kien thirc bai 1 va bai 2. • Khic sau mdt sd kien thiic : Menh de, menh de phu dinh, menh di keo theo, dinh If,... 2. KT nang Hgc sinh se cd kT nang phat hien va xu If tinh hudng trong viec giai toan Bia't phat bieu mdt dinh If dudi nhieu dang khac nhau. Xac dinh mdt each nhanh chdng dieu kien cin, dieu kien dii, dieu kien can va du cua menh de chiia bie'n trong mdt dinh li. 3. Thai do • Bie't van dung menh de trong suy luan Idgic. Dian dat cac dinh If, menh de mdt each mach lac, rd rang. n. CHUAN BI CUA GV VA HS 1. Chuan hi cua GV: Chuan bi kT cac cau hdi cho cac bai tap Chuin bi phin mau, va mdt so cdng cu khac. 2. Chuan bi cua HS : Cin dn lai mdt so kien thiic da hoc d bai 1, bai 2. Dgc bai kT d nha, xem lai ta't ca cac vf du va\Hj trong 2 bai nay. Xem lai cac bai tap ciia 2 bai trudc m . PHA N PH6 I TH6 I LUONG Bai nay day trong 2 tia't: Tiet ddu: chiia cdc bdi tap tiit 12 de'n 17. Tiet sau : chiia cdc bdi tap edn Iqi. 45 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com IV TIEN TRINH DAY HOC A. Bai cu Cau hoi 1 Hay nau diau kien cin va dieu kien du ciia menh de sau: a) Neu hai tap hgp A va B bing nhau thi mgi x thudc A deu thudc B va ngugc lai. b) Na'u n chia ha't cho 9 thi n chia ha't cho 3. Cau hoi 2 Hay nau menh da dao cua manh de sau: a) Neu hai tap hgp A va B bing nhau thi mgi x thudc A deu thudc B va ngugc lai. b) Ne'u n chia ha't cho 9 thi n chia ha't cho 3. B. Bai mdi HOAT DONG 1 Bai 12. Hoat ddng cua GV Cau hoi 1 • Hay xem cac cau trdn cd tinh diing - sai hay khdng? • Phan biet menh de diing va menh da sai. GV: Ggi 2 HS trd Idi. Hoat dong cua HS HS cd the tra Idi nhieu phuong an. Ggi y tra Idi cau hdi 1 • 2 - 1 chia hat cho 5: la menh diing • So 153 la hgp sd': la menh de sai. • hai cau con lai khdng la mdnh de. HOATD0NG2 Bai 13. Hoat ddng ciia GV Hoat dong ciia HS Cau hdi 1 Neu P diing thi menh de phii 46 HS cd the tra Idi nhidu phuang an. Ggi y tra Idi cau hoi 1 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com dinh P ciia nd dung hay sai? Cau hdi 2 Neu P sai thi menh de phu dinh P ciia nd diing hay sai? Cau hdi 3 Menh de phu dinh ciia manh da P la menh de nao ? Cau hdi 4 Hay nau cac menh de phii dinh trong bai tap. GV: Goi S HS trd Idi. Neu P diing thi menh de phii dinh P ciia nd sai. Ggi y tra Idi cau hdi 2 Ne'u P sai thi menh de phii dinhP cua nd dung. Ggi y tra Idi cau hdi 3 Menh de phii dinh ciia menh da P la manh di P. Ggi y tra Idi cau hdi 4 a) Tir giac ABCD da cho khdng phai la mdt hinh chii nhat; b)Sd9801lahgpsd'. HOAT DONG 3 Bai 14. Hoat dong ciia GV Hoat dong cua HS Cau hoi 1 Hay phat bieu menh de dudi dang P => Q. Cau hdi 2 Xet tinh diing sai ciia menh d^ tran. GV: Ggi 2 HS trd Idi. Ggi y tra Idi cau hdi 1 Neu tii giac ABCD cd tong hai gdc ddi la 180° thi tii giac dd ndi tie'p trong mdt dudng trdn Ggi y tra Idi cau hdi 2 Day la menh de diing. 47 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com HOAT DONG 4 Bai 15. Hoat dong ciia GV Cau hoi 1 Hay phat bieu menh de dudi dang P => Q. Cau hoi 2 Xet tfnh diing sai cua cac menh de P va Q. Cau hdi 3 Xet tfnh diing sai cua cac menh da P => Q. GV: Ggi 3 HS trd Idi. Hoat dong ciia HS Ggi y tra Idi cau hdi 1 Ne'u 4686 chia he't cho 6 thi 4686 chia ha't cho 5. Ggi y tra Idi cau hdi 2 Menh de P diing, menh de Q sai. Ggi y tra Idi cau hdi 3 Day la menh da sai do menh de P diing, menh de Q sai. HOAT DONG 5 Bai 16. Hoat dong ciia GV Hoat ddng cua HS Cau hoi 1 Hay tim menh de P. Cau hdi 2 Hay tim menh de Q. GV: Ggi 2 HS trd Idi. 48 Ggi y tra Idi cau hdi 1 Manh de P : "Tam giac ABC la tam giac vudng tai A" Ggi y tra Idi cau hdi 2 Manh da Q : "Tam giac ABC cd A5^ + AC^=5C^ " Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com HOAT DONG 6 Bai 17. Hoat ddng cua GV Cau hoi 1 Hay xac dinh P(0), P(l), P(2), P(-l). Cau hdi 2 Xac dinh tinh diing sai cua e). Cau hdi 3 Xac dinh tinh diing sai cua g) GV: Chia hoc sinh thdnh 4 nhdm ldm bdi, 3 nhdm ldm vd cic dqi dien trd led, nhom con iqi nhan xet ba nhdm tren. Ddp dn: a) Diing; b) Diing; c) Sai; Hoat dong ciia HS Ggi y tra Idi cau hdi 1 Menh de : P(0):0 = 0; P(l): 1 = 1; P(2): 2 = 4; P(-l): - 1 = 1 Ggi y tra Idi cau hdi 2 e) diing vi P(0), P(l) diing. Ggi y tra Idi cau hdi 3 g) sai vi P(2), P(-l) sai. d) Sai; e) Diing; g) Sai. HOAT DONG 7 Bai 18. Hoat dong cua GV Hoat ddng ciia HS Cau hoi 1 Tra Idi cau a) Cau hdi 2 Tra Idi cau b) Ggi y tra Idi cau hdi 1 Cd mot HS trong ldp em khdng thfch mdn Toan. Ggi y tra Idi cau hdi 2 Moi HS trong ldp em ddu bia't may tinh. 4-TKBGDAIS6lONC-T1 49 Tron Bo SGK: htts://bookiaokhoa.com Cau hdi 3 Download Ebook Tai: https://downloadsachmienphi.com Ggi y tra Idi cau hdi 3 Tra Idi cau c) Cau hdi 4 Tra Idi cau d) GV: Chia hgc sinh thdnh 4 nhdm ldm bdi, mdi nhdm ldm vd cii: dqi dien trd Idi. Cd mdt HS trong ldp em khdng bie't da bdng. Ggi y tra Idi cau hdi 4 Mgi HS trong ldp em deu da dugc tim bien HOAT DONG 8 Bai 19. Hoat ddng cua GV Hoat dong cua HS Cau hdi 1 Tra Idi cau a) Cau hdi 2 Tra Idi cau b) Cau hdi 3 Tra Idi cau c) 50 Ggi y tra Idi cau hdi 1 Day la menh de diing, ching ban X = 1, X = -1 thi X =1 . Menh de phii dinh ciia menh da nay la: VXGR,X^^1 . Ggi y tra Idi cau hdi 2 Day la menh da diing, ching han: n = 0, n = 1. Menh di phii dinh la : VX G N , n(n + 1) khdng la sd chfnh phuang. Ggi y tra Idi cau hdi 3 Day la menh de diing, ching han: khi X = 1. Menh de phii dinh la : 3x e R, (X- l)^=x - 1. Tron Bo SGK: htts://bookiaokhoa.com Cau hdi 4 Download Ebook Tai: https://downloadsachmienphi.com Ggi y tra Idi cau hoi 4 Tra Idi cau d) GV: Chia hgc sinh thdnh 4 nhdm ldm bdi, mdi nhdm ldm vd cii dqi dien trd Idi. Day la menh de diing, vi: khi n = 2k, k G N thi n^ + 1 = 4k'^ + 1 khdng chia het cho 4. Khi n le nghTa la n = 2k + 1, k G N, ta cd n^ + 1 = 4k^ + 4k + 2 khdng chia hat cho 4. Menh de phii dinh la : 3n G N, n + 1 khdng chia ha't cho 4. Day la menh de diing. HOAT DONG 9 Bai 20. Hoat dong cua GV Hoat dong cua HS Cau hoi 1 Khang dinh (A) diing hay sai? Cau hdi 2 Khang dinh (B) diing hay sai? Cau hdi 3 Khing dinh (C) diing hay sai? Cau hdi 4 Khang dinh (D) diing hay sai? GV: Chia hgc sinh thdnh 4 nhdm ldm bdi, mdi nhdm ldm vd cii dqi dien trd Idi. Ggi y tra Idi cau hdi 1 khi X = 1, ta dugc menh de sai. Vay (A) sai. Ggi y tra Idi cau hdi 2 Khix=v 2 ta dugc menh de diing. vay (B) diing. Ggi y tra Idi cau hdi 3 Ta tha'y x = ± v2 thi ta deu cd X- = 2. vay (C) sai. Ggi y tra Idi cau hdi 4 Khi X = 7, ta dugc menh da sai. Vay (D) sai 51 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Ddp dn: Chgn (B). Chii y ddy Id cdu hdi trdc nghiem, do dd ve nguyen tdc chi can chi ra phuang dn dung Id du. Song neu gidi thich them thi cdng khdc sau kien thitc han. HOAT DONG lO Bai 21. Hoat ddng ciia GV Cau hdi 1 Ta loai ngay cac cau nao? Cau hdi 2 Hay xem xet cau (C) Cau hdi 3 Hay chgn phuong an. GV: Chia hgc sinh thdnh 4 nhdm ldm bdi, 3 nhdm ldm vd cii dqi dien trd Idi, nhdm edn lai nhdn xet bdi ldm cua 3 nhdm tren. 52 Hoat dong cua HS Ggi y tra Idi cau hdi 1 (B) va (D) bi loai vi cd lugng tii tdn tai. Ggi y tra Idi cau hdi 2 cau (C) khdng phai la menh di tren vi cd rit nheu ngudi cao trdn Im 80 khdng la ciu thu bdng ro. Ggi y tra Idi cau hdi 3 Chgn (A). Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com §3. Tap hdp va cac phep toan tren tap hdp (tiet 5, 6) I. MUC TIEU 1. Kien thurc Giiip HS Hieu dugc hai each cho tap hgp: Liet ka cac phan tii cua tap hgp va neu tfnh chat dac trung cac phan tii ciia tap hgp. Bia't va van dung dugc cac phep toan ciia tap hgp: Phep hgp, phep giao, phep trur va phep la'y phan bii ciia tap hgp con. • Bia't tu duy linh boat khi diing cac each khac nhau de cho mdt tap hgp. Biet ^iing cac kf hieu ngdn ngii tap hgp de dian ta cac dieu kien bing Idi ciia mdt bai toan va ngugc lai. Bia't each tim giao, hgp, phan bii, hieu ciia cac tap hgp da cho va md ta tap hgp tao dugc sau khi da thuc hien xong phep toan. Bie't sir dung cac ki hieu va phep toan tap hgp de phat bieu cac bai toan va dian dat suy luan toan hgc mdt each sang siia, mach lac. Biet su dung bieu dd Ven de bieu dian quan he giiia cac tap hgp va cac phep toan tran tap hgp. 2. KT nang KT nang phat hien va'xu If tinh hudng trong viec giai toan. KT nang xac dinh cac tap hgp qua cac phep toan tran tap hgp. KT nang xac dinh mdt each nhanh chdng mdt phin tur nao dd cd thudc tap hgp da cho hay khdng? • KT nang tim hoac xac dinh cac tap con ciia mot tap hgp. van dung cac phep toan tren tap hgp de thuc hanh giai cac bai toan thuc ta'. 3. Thai do. Tir viec lam cac phep toan ve tap hgp lam cho hgc sinh yau thuc te cude sdng, lian he toan hgc vdi ddi sdng, biet van dung cac tinh hudng thuc ta' vdi toan hgc. 53 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Hgc sinh se bia't hinh thanh cac dang If thuya't mdi thdng qua tap hgp, dac biet la cac bai toan ve trd choi. Va tu duy: hgc sinh se cd tu duy va If luan chat che hon. IL CHUAN BI CUA GV v A HS 1. Chuan bi ciia GV: Chuin bi kT cac cau hdi cho cac bai tap thdng qua mdt sd bai toan thuc ta'. Chuan bi phin mau va mdt sd cdng cu khac. GV nan chuan bi ve san mdt so hinh tii 1.1 da'n 1.5. Chuan bi san mdt sd bang cd the hien cac bieu do Ven. Dac biet la bieu do Ven ciia vf du 1. • Chuin bi bang the hien d muc 3 de gidi thieu. 2. Chuan bi cua HS : • Cin dn lai mdt so kien thiic da hgc d bai 1, bai 2. HS : On lai mdt sd kie'n thiic ve tap hgp so. Xem lai cac bai tap cua 2 bai trudc. i n . PHA N PHOI THCJI LUONG Bai nay chia lam 2 tiet: Tie't ddu: Til ddu den hit muc 3. Tiet sau : Phdn edn Iqi vd hudng ddn bdi tap. IV TIEN TRINH DAY HOC A. Dat van de Cau hoi 1 Hay chi ra cac phin tii cua tap hgp : cac so nguyan to nhd hon 20. Cau hoi 2 Hay nau tfnh chit chung ciia cac so sau: 1 va -1 . 54 Tron Bo SGK: htts://bookiaokhoa.com B. Bai mdi Download Ebook Tai: https://downloadsachmienphi.com HOATDONG 1 1. Tap hgp GV : Ldy lai hai vi du trong cdu hdi kiem tra bdi cd de md td khdi niem tap hcfp. Neu a la phin tu cua tap hgp X, ta via't a G X (dgc la : a thudc X). Na'u a khdng phai la phan tur cua X, ta via't a ^ X (dgc la : a khdng thudc X). /) Liet ke cdc phdn tit cua tap hqp. GV: Hudng ddn HS thuc hien |H1| (muc dich cua |H1| Id nhdn mqnh y mdi phdn tu cua tap hap chi liet ke mot ldn). Hoat ddng ciia GV Cau hdi 1 Tap hgp cho d tren dugc cho bdi each nao? Cau hdi 2 Mot tap hop cd the cd hai phin tur gid'ng nhau khdng ? GV : Ggi 2 HS trd Idi. Gai y trd Idi : Hoat ddng ciia HS Ggi y tra Idi cau hdi 1. HS cd the tra Idi nhieu phuong an. Cac cau ggi y tra Idi Cach thii nhat : Liet kd cac phin tii ciia tap hgp. Ggi y tra Idi cau hdi 2. Khdng. A = {k; h; d; n; g; c; o; i; q; u; y; o; d; 1; a; p; t; u; d}. 55 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com 2) Chi rd cdc tinh chdt ddc trung cho cdc phdn tvt ciia tap hqp GV : Hudng ddn HS thuc hien\\\2\(muc dich ciia |H2 | Id luyen tap viec cho mot tap hap bdng hai cdch neu tren). Hoat ddng ciia GV Cau hoi 1 Tap hop cho d a) dugc cho bdi each nao? Cau hdi 2 Tap hop cho d b) dugc cho bdi each nao? Cau hdi 3 Em cd nhan xet gi vi cac so cho d tap hgp B GV: Ggi 3 HS trd Idi. Gai y trd Idi a) A ={3; 4; 5; 6; 7; 8;...; 20}. Hoat ddng ciia HS HS cd the tra Idi nhieu phuong an. Cac cau ggi y tra Idi Ggi y tra Idi cau hdi 1. Cach thii 2 : Chi ro cdc tinh chdt ddc trung cho cdc phdn ti( ciia tap hop. Ggi y tra Idi cau hdi 2 Cach thii nha't: Liet ka. Ggi y tra Idi cau hdi 3 Cac so d tap B la cac so nguydn chia he't cho 5, cd gia tri tuydt ddi nhd hon 16. b)B= {UG Z 1 lnl< 15, n chia het cho 5}. Chii y ve tap rong: Tap hgp khdng cd phan tii nao ta ggi la tap rdng va kf hieu 0 . Tap rdng la duy nha't. 56 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com HOAT DONG 2 Tap con va tap hgp bing nhau 2. a) Tap con Tap A duac ggi la tap con cua tap B vd ki hieu Id A c B ne'u mdi phdn tif cua tap A deu Id rrigt phdn tit cua tap B. GV : Cho hgc sinh chi ra mdt vdi tap con cua cdc tap A vd B trong\H2\. Sau dd dUa ra ki hieu sau ddy: Na'u A c B thi ta edn ndi tap A bi chiia trong tap B hay tap B chiia tap A va viet la B z) A. Tii dinh nghTa da thiy tfnh chit bic ciu sau day : (A c B va B c C) ^ A c C. GV : Cho hgc sinh chdng minh tinh chdt bdc cdu bdng dinh nghia. Ngudi ta coi 0 la tap con ciia mgi tap hgp, tiic la 0 c A vdi mgi tap A. Tir dinh nghTa ta thiy mdi tap hgp la tap con ciia chfnh nd. GV : Cho HS ldm bdi tap trdc nghiem sau: Cho A = {1;2;3},B = N, C = Z. Chgn ka't qua sai trong cac ke't qua sau (a) A c B; (c) A c C; Ddp dn: Chgn (d). GV : Hudng ddn HS thuc hien\H2 Hoat ddng cua GV Cau hoi 1 Cac tap hgp A va B dugc cho (b) B c C (d) ca 3 cau tran deu sai. Hoat ddng cua HS HS cd the tra Idi nhidu phuong an. Cac cau ggi y tra Idi 57 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com bdi each nao? Cau hdi 2 Em hay thii kiem tra xem khi la'y mdt phin tir b tap A (hoac B) bat ki thi phin tu dd cd thudc tap B (hoac A) hay khdng? GV : Ggi 2 HS trd Idi. Ddp dn: B c A. b) Tap hqp bdng nhau Ggi y tra Idi cau hoi 1 Cach thii 2 : Chi ro cdc tinh chdt dac trung cho cdc phdn tic ciia tap hap Ggi y tra Idi cau hdi 2 Mdi phan tu m thudc B thi m chia het cho 12, khi dd hien nhien m chia he't cho 6, tiic la m thudc A. Ngoai ra, ta cd the chi ra mdt vai so thudc A nhung khdng thudc B: ching han 6, 18,... Hai tap A va 5 dugc ggi la bing nhau va ki hieu M A = B neu mdi phin tur ciia A la mdt phan tii cua B va mdi phin tii ciia B ciing la mdt phin til cua A. Tur dinh nghia ta cd A = BoAcBvaBcA . Hai tap hgp khac nhau neu cd mdt phin tu ciia tap nay khdng la phan tii ciia tap kia. Hai tap hgp A va B khdng bing nhau (hay khac nhau) dugc kf hieu la A ;^ B. GV : Dua ra nhdn xet: Hai tap hap khdc rdng vd khdc nhau khi ta chi ra duqc cd mot phdn tit ciia tap ndy khdng thudc tap kia. GV : Hudng ddn HS thuc hien H4 . Hoat ddng ciia GV Cau hdi 1 Day cd phai la bai toan chimg minh hai tap hgp bing nhau khdng ? 58 Hoat ddng ciia HS HS cd the tra Idi nhidu phuong an. Ggi y tra Idi cau hdi 1 Phai Tron Bo SGK: htts://bookiaokhoa.com Cau hdi 2 Download Ebook Tai: https://downloadsachmienphi.com Ggi y tra Idi cau hdi 2 Ne'u CO, hay nau hai tap hop dd. GV : Goi 2 HS trd Idi. Ddp dn: A = {Tap hgp cac diam each deu hai miit cua mot doan thing}; B = {Dudng trung trirc ciia doan thing dd}. Ddy chinh Id bdi todn chdng minh hai tap hap diem bdng nhau. Tap hgfp thd nhdt Id tap cdc diem cdch deu hai miit cua doqn thdng dd cho. Tap thd hai Id tap hap cdc diem ndm tren dudng trung trite ciia doqn thdng dd cho. Luu y rdng, bdi todn tim quy tich (tim tap hgp diem) thudng dugc dua ve bdi todn chdng minh hai tap hgp bang nhau. c) Bieu do Ven Hinh 1.1 the hien A la tap con ciia tap B. Cach ve nhu vay la mdt bieu do Ven. Ngudi ta thudng dung bieu do Ven de md ta true quan md'i quan he ciia hai tap hgp, cac phep toan tran tap hgp. GV : Hudng ddn HS thuc hien vi du 1 vd |H5 Hoat ddng ciia GV Hinh LI Hoat ddng cua HS GV : Neu bieu dd Ven dd chuan bi sdn a nhd nhung khdng viet tap hgp vdo bdng. Ggi mot hoac 2 HS len dien ten cdc tap hgp. HS lan bang dien ten cac tap hgp vao bang da ve bieu do Ven. 59 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com HOAT DONG 3 3. Mot so cac tap con cua tap hgp sd thuc GV : treo bdng dd chuan bi (trang 18 SGK). Chu y nhdn mqnh cdc ki hieu khoang doqn, nita khoang. GV : Nen thuc Men muc ndy theo kieu trd chai nhu sau: - Cho hgc sinh dgc bang tran trudc. - Treo hai day so do bieu dian tran true so, cac true gid'ng nhau nhung b hai cdt thay doi thii tu cac so dd. - Trong thdi gian 1' cho 2 HS lan bang dien cac khoang hay niia khoang d cdt giira vao ban canh so do. - Dem cac ka't qua diing va cho diem. GV : Hudng ddn HS thuc hien\H6\ (\H6\nen thuc hien theo kieu trd chai nhU tren. Muc dich cua |H6| Id nhdm cung cd cdc khdi niem khoang, doqn, nua khoang. Phdn ndy giiip cho HS hgc tdt cdc chuang tiep theo). HOAT DONG 4 4. Cac phep toan tren tap hgp a) Phep hgp Hgp ciia hai tap hgp A va B, kf hieu la A u B, la tap hgp bao gom ta't ca cac phan tu thudc A hoac thudc B. AUB={X|XG A hoac x G B} GV : Hudng dan HS thitc hien vi du 2. Hoat ddng cua GV Cau hdi 1. 60 Hoat ddng ciia HS Ggi y tra Idi cau hdi 1 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com GV : Cho HS ldm bdi todn sau: Cho X e A LJ B. Hay chgn cau tra Idi diing trong cac cau sau: (a) X G A; (b) X G B (c) XG A va XG B; (d) XGA hoac XG B. Cau hdi 2. Cho A u B = [-2; 3 ). Hay la'y A va B. GV : Chia lap thdnh 4 nhdm, cdc nhdm bdn bqc vd cho ke't qua. b) Phep giao HS dien nhanh su lua chgn vao nira td gia'y. Dap. Chgn (d) Ggi y tra Idi cau hoi 2 HS cd the cho rat nhieu ke't qua khac nhau. A va B co the khac nhu d vf du 4. Giao ciia hai tap hgp A va B, kf hieu la A n B, la tap hgp bao gom tat ca cac phin tur thudc ca A va B. AnB={x|xG A va XGB} . GV : Hudng ddn HS thuc hien vi du 3. Hoat ddng ciia GV Cau hdi 1. GV : Cho HS ldm bdi todn sau: Cho X G A n B. Hay chgn cau tra Idi diing trong cac cau sau: (a) X G A; (b) X e B (c) XG A va XG B; (d) XG A hoac XG B. Hoat ddng cua HS Ggi y tra Idi cau hdi 1 HS dien nhanh su lua chgn vao nira td gia'y. Dap. Chgn (c) Tron Bo SGK: htts://bookiaokhoa.com 61 Download Ebook Tai: https://downloadsachmienphi.com Cau hdi 2. Cho A o B = [1; 2]. Hay la'y AvaB. GV : Chia lap thdnh 4 nhdm, cdc nhdm bdn bqc vd cho ke't qua. GV : Hudng ddn HS thuc hien H7 . Hoat ddng cua GV Cau hdi 1. GV : Cho HS md td bang Idi vd ggi 2 HS ditng tai chd trd Idi. Hay md ta A u B Cau hdi 2. Hay md ta A n B. GV : Cho HS md td bdng Idi vd ggi 2 HS ddng tai chd trd lai. Ddp dn : Ggi y tra Idi cau hoi 2 HS cd the cho rat nhieu ket qua khac nhau. A va B cd the khac nhu dvidu 5. Hoat dong cua HS Ggi y tra Idi cau hdi 1 HS cd the cd nhieu each phat bieu Ggi y tra Idi cau hoi 2 HS cd the cho nhieu each phat bieu. A u B la tap hgp cac HS gidi mdn Toan hoac mdn Van. A n B la tap hgp cac HS gidi ca mdn Toan va mdn Van. c) Phep lay phdn bit Cho tap A la tap con cua tap E. Phin bii cua A trong E, kf hieu la CfA, la tap hgp ta't ca cac phin tu ciia E ma khdng la phin tu cua A. GV : Hudng ddn HS thuc hien vi du 4 vd cho HS ldm HD sau: 62 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Hoat ddng ciia GV Cau hdi 1. GV: Cho HS ldm bdi todn sau: Cho X G C^A. Hay chgn cau tra Idi diing trong cac cau sau: (a) X G A; (b) (b) X ^ E (c) XG A va XG E; (d) XGE V X ^ A . Cau hdi 2. Cho CE A = Z" Hay lay A va E. GV: Chia lap thdnh 4 nhdm. Cdc nhdm bdn bqc vd bdc cdo ke't qua. GV : Hudng ddn HS thUc hien\\\^ . Hoat ddng ciia GV GV : Chia lap thdnh 4 nhdm: 2 nhdm ldm cdu a) vd 2 nhdm ldm cdu b). Ldn lugt cho dqi dien 2 nhdm len trinh bdy vd dien kit qua. Dap an: a) QjQ la tap hgp cac sd vd ti. Hoat ddng ciia HS Ggi y tra Idi cau hdi 1 HS dien nhanh sir lira chgn vao nira td gia'y. Dap. Chgn (d) Ggi y tra Idi c^u hoi 2 HS cd th^ cho rat nhi^u ket qua khac nhau. A va E cd the khac vdi ke't qua d vf du 6. Hoat ddng cua HS Sau khi thao luan, cac nhdm trinh bay ka't qua ra giay cu dai dian tra Idi b) C^Ala tap hgp cac HS nir trong ldp em. CQAM tap hgp cac HS nam trong trudng em ma khdng la HS ldp em. 63 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com d) Hieu cua hai tap hgp Hieu ciia hai tap hgp A va B, kf hieu la A\ B, la tap hgp bao gom tat ca cac phin tur thudc A nhung khdng thudc B. A\B = {x |x G A va x 5^ B}. GV : Hudng ddn HS thuc hien vi du S vd cho HS thuc hien HD sau: Hoat ddng ciia GV Cau hdi 1. GV : Cho HS ldm bdi todn sau: Cho x G A \ B. Hay chgn cau tra Idi diing trong cac cau sau: (a) x G A; (b) X G B (c) XGA va x e B; (d) XGA va x^ B. Cau hdi 2. Cho A \ B = (1; 2). Hay lay A vaB. GV : Chia lap thdnh 4 nhom, cdc nhdm bdn bae vd cho ke't qua. 64 Hoat ddng ciia HS Ggi y tra Idi cau hdi 1 HS diin nhanh su lua chgn vao niia td gia'y. Ddp. Chgn (d) Ggi y tra Idi cau hdi 2 HS cd the cho rat nhieu ket qua khac nhau. A va B cd the khac nhu d vi du 7. Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com TOM TAT BA I HOC 1. Ta thudng cho mdt tap hgp bing hai each sau : 1) Liet ka cac phin tur cua tap hgp. 2) Chi rd cac tfnh chit dac trUng cho cac phin tii ciia tap hgp. 2. Tap A dugc ggi la tap con ciia tap B va kf hieu la A c B ne'u mdi phin tii cua tap A deu la mdt phin tit cua tap B. 3. Hai tap A va B dugc ggi la bing nhau va kf hiau la A = B n^u mdi phin tii ciia A la mdt phin tii ciia B va mdi phin tii cua B ciing la mdt phin tur cua A. 4. Hgp ciia hai tap hgp A va B, kf hieu la A u B, la tap hgp bao g6m tit ca cac phin tii thudc A hoac thudc B. AUB={X|XG A hoac x G B). 5. Giao ciia hai tap hgp A va B, kf hieu la A n B, la tap hgp bao gdm tit ca cac phin tit thudc ca A va B. A n B = {X I X G A va x G B}. 6. Cho tap A la tap con ciia tap E. Phin bu cua A trong E, kf hieu la CgA, la tap hgp ta't ca cac phin tu: cua E ma khdng la phin tu ciia A. 7. Hiau ciia hai tap hgp A va B, kf hiau la A \ B, la tap hgp bao gom ta't ca cac phin tii thudc A nhung khdng thudc B. A\B = {x|x G A va x «? B}. 5-TKBGOAIS610NC-T1 65 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com MOT SO CAU HOI TRAC NGHlfeM 1. Cho tap hgp S = {x GMI X - 3x + 2 = 0}. Hay chgn ket qua diing trong cac ka't qua sau day (a)S={l,0} (c) S={0,2} (b)S={l,-l} (d)S={l,2}. Hay ghep mdi tap hgp d cdt ban trdi vdi mdi cdt d ben phai de dugc cSp hai tap hgp bang nhau (a)0 (b) A = (Tap hgp cac tam giac cd ba canh bing nhau} (c)B ={XGR|X ^ + X- 2 = 0 } (d)C={2n+l} . (1) E = {Tap hgp cac tam giac cd ba gdc bing nhau} (2) F = {Tap hgp cac tam giac cd hai gdc vudng} (3)S={1,2} (4) K ={Tap hgp cac sd tu nhian le} 3. Hay diin diing (D), sai (S) vao d vudng sau mdi cau sau 1) Cho A = Tap hgp cdc sd nguyen to chdn thi (a)A = 0 DiingO SaiQ; (b)A={2} DiingD SaiD; (c) A^ 0 DiingD SaiD; (d)A = {-2;2} DiingQ SaiQ 2) Cho A = {Tap hgp cdc tam gidc edn}; B = {Tap hgp cdc tam gidc cd 3 dudng cao bdng nhau}. Khi dd : (a)AcB Du,ngn SaiQ; (b)A = B DiingD SaiD; 66 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com (c)A3 B DiingD SaiD; (d) Ca ba cau deu sai Diing D Sai D ; 3) Cho A cB, khidd (a)VxGA=>x^ B DiingD SaiD; (b)VxGB=>xG A DiingD SaiD; (C)VXGA=>XG B DiingD SaiD; (d)xGA^xG B DiingD SaiD;- 4) Cho A = B, khi dd : (a)VxGA=>XGB DiingD SaiD; (b) Vx G A=:>x «£ B DiingD SaiD; (C)VXGB=>XG A DiingD SaiD; (d) Vx 5? B => X «? A DiingD SaiD; (e)Vx^A=>x^ B DiingD SaiD 4. Cho A = B, B c C. Hay chgn ket qua diing trong cac ket qua sau day (a) A = C; (b) A c C; (c) C c A; (d) cau (a) diing (b) sai. 5. Cho A c: B, B c C. Hay chgn ket qua diing trong mdi ket qua sau (a) A c C; (b) C c A (c) A = C; (d) ca 3 cau tran deu sai 6. Cho A = {1; 2;3}, B = N, C = Z. Hay chgn ket qua sai trong nhiing ket qua sau day: (a) A c B; (b) B c C (c) A c C; (d) ca 3 cau tran deu sai. 67 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Cho cac tap A, B, C nhu bai 13. Hay chgn ke't qua sai trong mdi ket qua sau. (a) Vx G A ^ X G B; (b) Vx G B => x G C; (c) Vx G A => X G C; (d) ca ba ciu tran deu sai Hay dien D, S sau mdi cau sau day: 8. (a)NcZn ; (b)EcQn ; (c)ZcQn; (d)QcNn Cho A = {Tap hgp cac sd tu nhian le} Hay chgn cau tra Idi diing trong 9. cac cau tra Idi sau. (a) A = 0 ; (b) (b) A c N; (c) Mgi X G A thi x chia ha't cho 3; (d) Vx G A thi X khdng chia ha't cho 2. Cho A = {Tap hgp cac sd tu nhien chin}; B = (Tap hgp cac sd tu nhien 10. chia het cho 3}; C = {Tap hgp cac sd tu nhian chia ha't cho 6}. Hay chgn ka't qua diing trong cac ket qua sau day: (a) A c B e C; (b) A c C va B c C; (c) A c C va A c B; (d) C c A va C c B. Hay ndi mdt cau d cdt ban trai vdi mdt cau d cdt ban phai de dugc mot 11. cau diing. (a) A = B khi va chi khi (1) mgi tap hgp G A (b) A c B khi va chi khi (c) A c: B va B c C thi (d) 0 la tap con cua 68 (2) Vx G A => X G B va Vx G B ^ X (3)Ac C (4) Vx G A =^ X 6 B. Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com 12. Hay dien vao d trd'ng (...) trong mdi cau sau de dugc ket qua diing. (a) Neu A = B thi A c B va B C (b) Na'u A c B, va B c C thi C A (c) Neu A c B va B.... C thi A = B (d)N Z Q M. 13. Cho A = {1, 2, 3}. Hay chgn cau tra Idi diing trong cac cau sau: (a) A cd 3 tap hgp con; (b) A cd 2 tap hgp con; (c) A cd 1 tap hgp con; (d) A cd 4 tap hgp con. Ddp dn: l-(d) 2. (a) va (2); (b) va (1); (c) va (3); (d) va (4) 1) (a) Sai; 2) (a) Sai; 3) (a) Sai; 4) (a) Diing; (b) Diing; (b) Sai; (b) Sai; (b) Sai; (c) Diing; (c) Diing; (c) Diing; (c) Diing; (d) Sai. (d) Sai. (d) Sai. (d) Diing (e) Diing, 69 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com HUONG DAN BAI TAP \ t NHA Bai 22. Hoat dong ciia GV Cau hoi 1. Giai phuang trinh: 2x - x^ = 0. Cau hdi 2. Giai phuang trinh: 2x^ - 3x - 2 = 0. Cau hoi 3 Hay liet ke cac phin tir cua A. C^u hdi 4 Hay liet ke cac phin tix ciia B. Bai 23. Hoat ddng cua GV Cau hoi 1. Hay chi ra tiiih chit cua tap A. Cau hdi 2. Hay chi ra tinh chit cua tap B. 70 Hoat dong cua HS Ggi y tra Idi cau hdi 1 Nghiem cua phuang trinh la : O; 1. Ggi y tra Idi cau hdi 2 Nghiam cua phuong trinh la : Ggi y tra Idi cau hdi 3 A={o;2,--i} Ggi y tra Idi cau hdi 4 B={2;3;4;5}. Hoat dong ciia HS Ggi y tra Idi cau hoi 1 Cac sd' cua A chi chia ha't cho 1 va chfnh nd. Dd la cac sd nguyen td' nhd hon 13. Ggi y tra Idi cau hdi 2 B la tap hgp cac sd nguyen cd gia tri tuyet ddi khdng vugt qua 3. Tron Bo SGK: htts://bookiaokhoa.com Cau hdi 3 Download Ebook Tai: https://downloadsachmienphi.com Ggi y tra Idi cau hoi 3 Hay chi ra tinh chit cua tap C. Bai 24. Hoat ddng cua GV C^u hoi 1. Hay giai phuong trinh: (x - l)(x - 2)(x - 3) = 0 Cau hoi 2. Hay chi ra A. Cau hdi 3 Hai tap hgp A va B cd bing nhau khdng ? Bai 25. Hoat dong cua GV Cau hoi 1. Xet hai tap A va B. C^u hoi 2. Xet hai tap A va C. C^u hoi 3 Xet hai tap B va D. Cau hoi 4 Xet hai tap C va D. C la tap hgp cac sd' nguyen n khdng nhd hon -5 , khdng ldn hon 15 va chia he't cho 5. Hoat dong cua HS Ggi y tra Idi cau hdi 1 Tap nghiem la S = {1;2; 3} Ggi y tra Idi cau hdi 2 A = S Ggi y tra Idi cau hoi 3 Khdng bing nhau. Hoat dong ciia HS Ggi y tra Idi cau hdi 1 B e A. Ggi y tra Idi cau hdi 2 CcA . Ggi y tra Idi cau hdi 3 B\D = {2},D\B = {4; 8}. hai tap nay khdng chiia nhau. Ggi y tra Idi cau hdi 4 CczD. 71 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Chii y rdng tap A chda tap B neu B\A = 0. Bai 26. Hoat dong cua GV Cau hdi 1. Hay md ta A n B. Cau hoi 2. Hay mdta A\B . Cau hoi 3 Hay md ta A L^ B. Cau hoi 4 Hay md ta B \ A. Hoat dong cua HS Ggi y tra Idi cau hdi 1 BcA=:>Ao B = B. A n B la tap hgp cac hgc sinh hgc tia'ng Anh cua trudng em. Ggi y tra Idi cau hoi 2 A \ B la tap cac hgc sinh khdng hgc tia'ng Anh ciia trudng em. Ggi y tra Idi cau hoi 3 A u B = A. la tap hgp hgc sinh trudng em Ggi y tra Idi cau hdi 4 B \ A = 0 . Tap khdng cd hgc sinh nao cua trudng em. \ = 0. Chii y rdng tap A chita tap B ne'u B\y Bai 27. Hoat dong cua GV C^u hdi 1. Hay xet A va B. Cau hdi 2. Hay xet B va C. 72 Hoat ddng ciia HS Ggi y tra Idi cau hdi 1 B c A Ggi y tra Idi cau hdi 2 C c B Tron Bo SGK: htts://bookiaokhoa.com Cau hdi 3 Download Ebook Tai: https://downloadsachmienphi.com Ggi y tra Idi cau hdi 3 Hay xet C va D. Cau hdi 4 Hay xet D va E. Cau hdi 5 Hay xet F va E. Ddp dn: Sit dung tfnh chit bic cau, ta cd: DcC . Ggi y tra Idi cau hdi 4 EcD . Ggi y tra Idi cau hdi 5 FcE . a)Fc:Ec=CciA;FcDc:CcA;Bc:A ; b) D n E = F Chii y rang tap A chira tap B neu B \ A = 0 . Bai 28. Hoat ddng ciia GV Cau hoi 1. Tim tap hgp (A \B). Cau hoi 2. Tun tap hgp (B\ A). Cau hoi 3 Tim tap hgp (A\B)^(B\A ) Cau hoi 4 Tim tap hgp (AuB)\(AnB) . cau hoi 5 Hoat dong cua HS Ggi y tra Idi cau hdi 1 (A\B)={5}. Ggi y tra Idi cau hdi 2 (B\A)={2 } Ggi y tra Idi cau hdi 3 (A\B)^(B\A) = {2; 5} Ggi y tra Idi cau hdi 4 A u B= {1;2;3;5},A n B= {1; (A u B)\(A n B)= {2; 5). 3}, 73 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Hai tap hgp nhan dugc la bing nhau hay khac nhau ? Ggi y tra Idi cau hoi 5 (A\B) u (B\ A) = (A u B)\(A n B). Bai 29. Hoat dong cua GV Cau hoi 1. Vx G R, X G (2,1; 5,4) => X G (2; 5), diing hay sai? Cau hdi 2. Vx G R, X G (2,1; 5,4) => X G (2; 6), diing hay sai? Cau hoi 3 Vx G R,-l,2 - 1 < X < 3, diing hay sai? cau hdi 4 Vx G R, -4,3 < X < -3,2 => - 5 < X < -3 . Bai 30. Hoat dong ciia GV Cau hoi 1. Tim A u B Cau hoi 2. Tim AoB. 74 Hoat dong ciia HS Ggi y tra Idi cau hdi 1 Sai. Ggi y tra Idi cau hoi 2 Diing Ggi y tra Idi cau hdi 3 Sai. Ggi y tra Idi cau hdi 4 Diing. Hoat dong cua HS Ggi y tra Idi cau hoi 1 A u B = [-5; 2) Ggi y tra Idi cau hdi 2 A n B = (-3; 1]. Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Luyen tap (tiet 7 va 8) I. MUC TifeU 1. Kie'n thiirc Giiip HS • On tap lai toan bd kie'n thiic ve tap hgp. • Bia't va van dung dugc cac phep toan ciia tap hgp: Phep hgp, phep giao, phep trur va phep la'y phin bii cua tap-hgp con. Bia't sur dung bi^u dd Ven di hiiu diin quan ha giiia cac tap hgp va cac phep toan tran tap hgp. 2. KT nang Hgc sinh se cd ki nang phat hien va xur If tinh hudng trong viec giai toan tap hgp dac biet la ki nang sii dung bieu dd Ven. Da'm sd phin tii cua tap hgp nhanh va chfnh xac thdng qua phep toan tran tap hgp. Van dung cac phep toan tran tap hgp d^ thuc hanh giai cac bai toan thuc te. 3. Thai do Bie't lian he giiia thuc tian ddi sdng vdi toan hgc. Nhan bia't su gin giii gitra toan hgc va cac mdn hgc khac. • Tfch cue, chu ddng, tu giac trong hgc tap. n. CHUAN BI CUA GV v A HS 1. Chuan bi cua GV: • Chuin bi ki cac cau hdi cho cac bai tap luyen tap. • Chuin bi pha'n mau va mdt sd cdng cu khac. - Chuan bi sin mdt sd bang cd the hian cac bia'u do Ven cho cac bai tap. GV: Chuin bi sin mdt bai kiim tra trie nghiem 10' 75 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com 2. Chuan hi ciia HS : Cin dn lai mdt so kia'n thiic da hoc d bai 3 Xem lai ta't ca cac vf du va [//J trong bai 3. HI. PHA N PHOI THd l LUONG Bai nay chia lam 2 tiet: Tie't 8: Chiia cdc bdi tap: 31, 32, 37 vd kiem tra 10' Tie't 9: Chiia cdc bdi tap 39, 40, 41 vd kiem tra trdc nghiem 10'. IV. TIEN TRINH DAY HOC A. Bai cu ChoA= {-3,-2,-1,0, 1,2, 3}; B= {-1,2, 3}; C= {-2,3,4,-4} Cau hoi 1 Hay xac dinh xem tap nao la tap con cua tap nao? Cau hoi 2 Hay xac dinh A u C, A n C. Cau hoi 3 Hay xac dinh A\ B, va CgA. B. Bai mdi HOAT DONG 1 Bai 31. Hoat dong cua GV Cau hoi 1. Hay ve so do Ven ciia cac sau day: P=(AnB ) ^(A\B ; Q = (AnB)u(B\A) . 76 tap Hoat dong ciia HS Ggi y tra Idi cau hdi 1 HS ve nhanh theo nhdm va thdng nha't. Tron Bo SGK: htts://bookiaokhoa.com Cau hdi 2. Download Ebook Tai: https://downloadsachmienphi.com Ggi y tra Idi cau hdi 2 Cd nhan xet gi vd P va Q. Cau hdi 3. Hay ap dung de giai bai toan nay. GV : Chia lap thdnh 4 nhdm. Hai nhdm ve bieu dd Ven thit nhdt, hai nhdm edn lai ve bieu dd Ven thd hai vd bao cdo ket qua. Ddp. P = A; B = Q. Ggi y tra Idi cau hdi 3 Ddp. A={1;3;5;6;7;8;9} , B= {2; 3; 6; 9; 10}. HOAT DONG 2 Bai 32. Hoat ddng ciia GV GV : Chia lap thdnh 4 nhdm. Hoat dong cua HS Cau hdi 1. (Danh cho 2 nhdm diu). Hay xac dinh A n (B \ C); (AnB)\C . Cau hdi 2. (Danh cho 2 nhdm sau). Hay ve so dd Ven ciia cac tap sau day: P = A n (B\C); Q = (A n B)\C. va nhan xet \i mdi quan he cua hai tap do. Ggi y tra Idi cau hdi 1 HS diing tfnh chat ciia phep toan de lam bai. Ddp. An(B\C) = (AnB)\C= {2; 9} Ggi y tra Idi cau hdi 2 Hoc sinh ve so dd Ven va di den ke't luan Ddp. P=Q . 77 Tron Bo SGK: htts://bookiaokhoa.com Download Ebook Tai: https://downloadsachmienphi.com Cha y : Ta cd the chiing minh dang thiic A n (B \ C) = (A n B) \ C diing cho ba tap A, B, C bit ki nhu sau : Giasiix G A n (B\C). Khidd x G A, x G (B\C) . Vay X G A, X G B, X g C. Tiic la X G A n B, X ^ C. Vay x G (A n B) \ C. Ngugc lai, gia sii x G (A n B) \ C tiic la X G (A n B), X ^ C hay x G A, X G B, X ^ C hay X G A, X G (B\C). vay x G A n (B\C). HOATD6NG3 Bai 37. Hoat dong ciia GV GV: Cd the chuan bi sdn 2 tap hgp sd A = la; a + 2J vd B = lb;b +1] vdo 2 bdng khdc nhau, sau do di chuyen ehiing de duge ,nhdn xet: Hoat dong ciia HS HS quan sat va dua ra nhan xet ban Ddp. b-2 a b + 1. Tur dd suy ra dieu kien da'AnB?!:01ab-2 """