Discrete Mathematics MCQs 2

 

For the following sets : Ø, A = {1,3 }, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}, insert the correct symbol between
5. Ø — B
a. =
b. ⊂
c. ⊄
d. ∈
Ans b.

6. A — B
a. =
b. ⊂
c. ⊄
d. ∈
Ans. C.

7. A—C
a. =
b. ⊂
c. ⊄
d. ∈
Ans b.

8. B—C
a. =
b. ⊂
c. ⊄
d. ∈
Ans b.

9. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}and A = {1, 3, 5, 7, 9}. Then A’ is —
a. {2, 4, 6, 8, 10}
b. {1, 2, 3, 6}
c. {2, 6}
d. {1, 4, 5, 6, 7, 8}
Ans a.

10. Let A = {2, 4, 6, 8} and B = {6, 8, 10, 12}. Then A∪B is—
a. {2, 5, 6, 10}
b. {2, 4, 6, 8, 10, 12}
c. {2, 4, 6, 8}
d. {2, 8, 10, 12}
Ans b.

11. If A = {a, e, i, o, u} and B = {a, i, u} then which is true
a. A∪B = A
b. A∩B = A
c. A⊂B
d. B⊆A
Ans a.

12. If x and y are two sets such that n(x∪y) = 50, n(x) =28 and n(y) = 32, find n(x∩y)
a. 10
b. 20
c. 30
d. 40
Ans a.

13. A statement is said to be a _______ if it is true for all logical possibilities.
a. theorem
b. tautology
c. anatomy
d. clause
Ans b.

14.If two simple statements p and q are connected by the world ‘and’ then the resulting compound statement “p and q” is called a ________.
a. conjunction
b. disjunction
c. set
d. complement
Ans a.

17. Chose the negation of the statement
p: New Delhi is a city.
a. ∼ p: New Delhi is a city
b. ∼ p: New Delhi is not a city
c. ∼ p: It is the case that New Delhi is a city
d. ∼ p: It is true that New Delhi is a city
Ans b.

18. Which is the negation of the following conjunction–
Paris is in France and London is in England
a. ∼ p: Paris is not in France, and ∼ q: London is not in England.
b. ∼ p∧q: Paris is not in France or London is not in England
c. ∼ p∧q: Paris is in France and London is not in England
d. ∼ p∧q: Paris is not in France or London is in England
Ans b.

19. Which is the negation of the following conjunctions:-
2+3 = 5 and 8<10.
a. ~ p: 2+3 = 5 and q: 8<10.
b. ~ p: 2+3 =5 and q: 8 =10
c. ~ p∧q = 2+3 ≠ 5 or (8<10)
d. ~ p∧q = 2+3 ≠ 5 and (8<10)
Ans c.

20. If a and b are any two elements of a group G, then the equations ax = b and ya = ______ have unique solutions in G.
a. b
b. a
c. a & b
d. y
Ans a.

21. If every element of a group G is its own inverse then G is _______
a. Unique
b. Same
c. Abelian
d. Alone
Ans c.