(1

BI TP MNH

Bai 1. Trong cc cu di y, cu no l mnh , cu no l mnh cha bin:

a) S 11 l s chn.

b) Bn c chm hc khng ?

c) Hu l mt thnh ph ca Vit Nam.

d) 2x + 3 l mt s nguyn dng.

e) .

f) 4 + x = 3.

g) Hy tr li cu hi ny!.

h) Paris l th nc .

i) Phng trnh c nghim.k) 13 l mt s nguyn t.

Bai 2. Trong cc mnh sau, mnh no l ng ? Gii thch ?

a) Nu a chia ht cho 9 th a chia ht cho 3.b) Nu th .

c) Nu a chia ht cho 3 th a chia ht cho 6.d) S ln hn 2 v nh hn 4.

e) 2 v 3 l hai s nguyn t cng nhau.

f) 81 l mt s chnh phng.

g) 5 > 3 hoc 5 < 3.

h) S 15 chia ht cho 4 hoc cho 5.

Bai 3. Trong cc mnh sau, mnh no l ng ? Gii thch ?

a) Hai tam gic bng nhau khi v ch khi chng c din tch bng nhau.

b) Hai tam gic bng nhau khi v ch khi chng ng dng v c mt cnh bng nhau.

c) Mt tam gic l tam gic u khi v ch khi chng c hai ng trung tuyn bng nhau v c mt gc bng .

d) Mt tam gic l tam gic vung khi v ch khi n c mt gc bng tng ca hai gc cn li.

e) ng trn c mt tm i xng v mt trc i xng.

f) Hnh ch nht c hai trc i xng.

g) Mt t gic l hnh thoi khi v ch khi n c hai ng cho vung gc vi nhau.

h) Mt t gic ni tip c ng trn khi v ch khi n c hai gc vung.

Bai 4. Trong cc mnh sau, mnh no l ng ? Gii thch ? Pht biu cc mnh thnh li:

a) .

b)

c) .

d) .

e) f)

g) .h)

i)

EMBED Equation.DSMT4

k) l hp s.

l) khng chia ht cho 3.

m) l s l.

n) chia ht cho 6.

Bai 5. in vo ch trng t ni "v" hay "hoc" c mnh ng:

a) .

b) .

c)

d) .

e) Mt s chia ht cho 6 khi v ch khi n chia ht cho 2 . cho 3.

f) Mt s chia ht cho 5 khi v ch khi ch s tn cng ca n bng 0 . bng 5.

Bai 6. Cho mnh cha bin P(x), vi x ( R. Tm x P(x) l mnh ng:

a)

b)

c)

d)

e)

f)

Bai 7. Nu mnh ph nh ca cc mnh sau:

a) S t nhin n chia ht cho 2 v cho 3.

b) S t nhin n c ch s tn cng bng 0 hoc bng 5.

c) T gic T c hai cnh i va song song va bng nhau.

d) S t nhin n c c s bng 1 v bng n.

Bai 8. Nu mnh ph nh ca cc mnh sau:

a)

.

b) .

c) .

d) .

e) .

f) .

g) khng chia ht cho 3.h) l s nguyn t.

i) chia ht cho 2.

k) l s l.

Bai 9. Pht biu cc mnh sau, bng cch s dng khi nim "iu kin cn", "iu kin ":

a) Nu mt s t nhin c ch s tn cng l ch s 5 th n chia ht cho 5.

b) Nu th mt trong hai s a v b phi dng.

c) Nu mt s t nhin chia ht cho 6 th n chia ht cho 3.

d) Nu th .

e) Nu a v b cng chia ht cho c th a + b chia ht cho c.

Bai 10. Pht biu cc mnh sau, bng cch s dng khi nim "iu kin cn", "iu kin ":

a) Trong mt phng, nu hai ng thng phn bit cng vung gc vi mt ng thng th ba th hai ng thng y song song vi nhau.

b) Nu hai tam gic bng nhau th chng c din tch bng nhau.

c) Nu t gic T l mt hnh thoi th n c hai ng cho vung gc vi nhau.

d) Nu t gic H l mt hnh ch nht th n c ba gc vung.

e) Nu tam gic K u th n c hai gc bng nhau.

Bai 11. Pht biu cc mnh sau, bng cch s dng khi nim "iu kin cn v ":

a) Mt tam gic l vung khi v ch khi n c mt gc bng tng hai gc cn li.

b) Mt t gic l hnh ch nht khi v ch khi n c ba gc vung.

c) Mt t gic l ni tip c trong ng trn khi v ch khi n c hai gc i b nhau.

d) Mt s chia ht cho 6 khi v ch khi n chia ht cho 2 v cho 3.

e) S t nhin n l s l khi v ch khi l s l.

Bai 12. Chng minh cc mnh sau bng phng php phn chng:

a) Nu th mt trong hai s a v b nh hn 1.

b) Mt tam gic khng phi l tam gic u th n c t nht mt gc nh hn .

c) Nu v th .

d) Nu bnh phng ca mt s t nhin n l mt s chn th n cng l mt s chn.

e) Nu tch ca hai s t nhin l mt s l th tng ca chng l mt s chn.

f) Nu mt t gic c tng cc gc i din bng hai gc vung th t gic ni tip c ng trn.

g) Nu th x = 0 v y = 0.(2

BI TP TP HPBai 1. Vit mi tp hp sau bng cch lit k cc phn t ca n:

A =

B =

C =

D =

E =

F =

G =

H =

Bai 2. Vit mi tp hp sau bng cch ch r tnh cht c trng cho cc phn t ca n:

A =

B =

C =

D =

E =

F =

G = Tp tt c cc im thuc ng trung trc ca on thng AB.

H = Tp tt c cc im thuc ng trn tm I cho trc v c bn knh bng 5.

Bai 3. Trong cc tp hp sau y, tp no l tp rng:

A =

B =

C =

D =

E =

F =

Bai 4. Tm tt c cc tp con, cc tp con gm hai phn t ca cc tp hp sau:

A =

B =

C =

D =

E =

Bai 5. Trong cc tp hp sau, tp no l tp con ca tp no?

a) A = ,B = ,C = ,D = .

b) A = Tp cc c s t nhin ca 6 ;B = Tp cc c s t nhin ca 12.

c) A = Tp cc hnh bnh hnh;

B = Tp cc hnh ch nht;

C = Tp cc hnh thoi;

D = Tp cc hnh vung.

d) A = Tp cc tam gic cn;

B = Tp cc tam gic u;

C = Tp cc tam gic vung;

D = Tp cc tam gic vung cn.

Bai 6. Tm A ( B, A ( B, A \ B, B \ A vi:

a) A = {2, 4, 7, 8, 9, 12}, B = {2, 8, 9, 12}

b) A = {2, 4, 6, 9}, B = {1, 2, 3, 4}

c) A = , B = .

d) A = Tp cc c s ca 12, B = Tp cc c s ca 18.

e) A = , B = Tp cc s nguyn t c mt ch s.

f) A = , B = .

g) A = , B = .

Bai 7. Tm tt c cc tp hp X sao cho:

a) {1, 2} ( X ( {1, 2, 3, 4, 5}.

b) {1, 2} ( X = {1, 2, 3, 4}.

c) X ( {1, 2, 3, 4}, X ( {0, 2, 4, 6, 8}d)

Bai 8. Tm cc tp hp A, B sao cho:

a) A(B = {0;1;2;3;4}, A\B = {3; 2}, B\A = {6; 9; 10}.

b) A(B = {1;2;3}, A\B = {4; 5}, B\A = {6; 9}.

Bai 9. Tm A ( B, A ( B, A \ B, B \ A vi:

a) A = [4; 4], B = [1; 7]

b) A = [4; 2], B = (3; 7]

c) A = [4; 2], B = (3; 7)

d) A = ((; 2], B = [3; +()

e) A = [3; +(), B = (0; 4)

f) A = (1; 4), B = (2; 6)

Bai 10. Tm A ( B ( C, A ( B ( C vi:

a) A = [1; 4], B = (2; 6), C = (1; 2)b) A = ((; 2], B = [3; +(), C = (0; 4)

c) A = [0; 4], B = (1; 5), C = (3; 1]d) A = ((; 2], B = [2; +(), C = (0; 3)

e) A = (5; 1], B = [3; +(), C = ((; 2)

Bai 11. Chng minh rng:

a) Nu A ( B th A ( B = A.

b) Nu A ( C v B ( C th (A ( B) ( C.

c) Nu A ( B = A ( B th A = B

d) Nu A ( B v A ( C th A ( (B ( C).

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