# Discrete Mathematics Multiple Choice Questions with Answers pdf

Discrete Mathematics MCQ Questions with Answers is a PDF booklet containing 50 MCQ questions and answers on topics such as counting, sets, sequences and permutations, probability, integration, and more.

The questions are designed to help students learn the basic concepts of discrete mathematics while also testing their knowledge.

Discrete Mathematics Multiple Choice Questions with Answers pdf for the preparation of MCA, BCA, and IT academic & competitive exams.

#### Brief Introduction to Discrete Mathematics

Discrete Mathematics is a branch of mathematics that deals with the representation of mathematical objects as discrete structures. Discrete structures can be finite or infinite and can be abstract or concrete.

Discrete mathematics is the study of algorithms and problems on these structures, as well as their properties.

#### Discrete Mathematics Multiple Choice Questions with Answers

1. If the number of elements in a set is not finite, then the set is called an

A) finite set

B) collective set

C) Infinite set

D) arranged set

Answer: C) Infinite set

2. If A = {1,3,5} and B = {1,3,5,7} then A is a …. subset of B

A) smaller

B) proper

C) improper

D) normal

Answer: B) proper

3. Consider the set A = {1, 2, 3}, the power set of A has …. elements

A) 23

B) 22

C) 25

D) 26

Answer: A) 23

4. The cardinality of the set A = {1, 2, 3, 0, 6, 7, 8, 9} is

A) 7

B) 8

C) 6

D) 2

Answer: B) 8

5. If A is the arithmetic mean between the extremes a and b then A =

A) a – b / 2

B) a + b / 2

C) a + 2b / 2

D) a – 2b / 2

Answer: B) a + b / 2

6. The nth term of an arithmetic progression a + (a + d) + (a + 2d) + …. is

A) a + nd

B) a + (n–1)d

C) a + (n+1)d

D) 2a + (n+1)d

Answer: B) a + (n–1)d

7. The proposition ~p ν (p ν q) is a

A) Tautology

B) Contradiction

C) Logical equivalence

D) None of the above

Answer: A) Tautology

8. The sum to infinity of a geometric progression is

A) a / 1 – r

B) a / 1 + r

C) – a / 1 + r

D) a2 / 1 + r

Answer: A) a / 1 – r

9. Combinatorics is the branch of discrete mathematics concerned with …..

A) counting problems

B) abstract algebra

C) derivative problems

D) integrated problems

Answer: A) counting problems

10. If the object A is chosen in m ways and B in n ways then either A or B is chosen in …. ways

A) m/n

B) mn

C) m + n

D) m – n

Answer: C) m + n

11. A relation means …… on a set S.

A) dual relation

B) binary relation

C) reflexive relation

D) symmetric relation

Answer: B) binary relation

12. A …. is a set S with a relation R on it which is reflexive, anti-symmetric, and transitive.

A) equivalent set

B) ordered set

C) implicit set

D) Partially ordered set

Answer: D) Partially ordered set

13. If S is a poset and a, b are in S such that a > b and there is no c in S such that a > c and c > b, then we say that …..

A) b covers b

B) a covers a

C) a covers b

D) b covers a

Answer: C) a covers b

14. Let (A,*) be an algebraic system where * is a binary operation on A. Then (A,*) is called a semigroup if it satisfies the

A) closure law

B) associative law

C) reflexive law

D) closure and associative law

Answer: D) closure and associative law

15. Let N be the set of natural numbers, under the operation ‘*’, where x*y = max (x,y). Then the set is a

A) top group

B) multigroup

C) semigroup

D) subgroup

Answer: C) semigroup

16. The set Z with the binary operation “subtraction” is …… a subgroup

A) not

B) subset of

C) always

D) superset of

Answer: A) not

17. If for any ring R, a.b = b.a for all a, b∈R then R is said to be a ……

A) integer ring

B) commutative ring

C) cyclic ring

D) non-commutative ring

Answer: B) commutative ring

18. A commutative ring is said to be an integral domain if it has no …….

A) zero-divisors

B) inverse

C) multiples

D) identity

Answer: A) zero-divisors

19. A ring R is said to be a ……. if x2 = x for all x∈R.

A) permutation ring

B) commutative ring

C) Boolean ring

D) identity ring

Answer: C) Boolean ring

20. If R is a Boolean ring then R is a …….

A) commutative ring

B) subring

C) integral ring

D) integer

Answer: A) commutative ring

21. Reasoning is a special kind of thinking called ….…

A) inferring

B) logics

C) bijective

D) contradictive

Answer: A) inferring

22. The basic unit of our objective language is called a …….

A) prime divisor

B) prime statement

C) bijective statement

D) statement

Answer: B) prime statement

23. The validity of an argument does not guarantee the truth of the ……

A) permutation

B) commutative value

C) conclusion

D) identity value

Answer: C) conclusion

24. A ……. is a statement that is either true or false, but not both.

A) argument

B) conclusion

C) bi-conditional

D) proposition

Answer: D) proposition

25. A function f: A → B is said to be …….. if for every yÎB there exists at least one element xÎA such that f(x) = y.

A) surjective

B) bijective

C) injective

D) Automorphism

Answer: A) surjective

26. If f is onto then f(A) =

A) Φ

B) B

C) A

D) A x B

Answer: B) B

27. The set {x ∈ R: a < x < b is denoted by

A) [a, b)

B) (a, b]

C) (a, b)

D) {a, b}

Answer: C) (a, b)

28. A function f: A→B is said to be a periodic function if …….

A) f(x) = f(α)

B) f(x) = f(x – α)

C) f(x) = f(x + 2α)

D) f(x) = f(x + α)

Answer: D) f(x) = f(x + α)

29. f(x) = tanx is a periodic function with period …….

A) π

B) 2π

C) π/2

D) 3π

Answer: A) π

30. If A = {2, 3, 4}, B = {4, 5, 6} and C = {6, 7} then Ax(C – B) =

A) {(2,7) (3,7) (7,4)}

B) {(2,7) (3,3) (4,7)}

C) {(7,2) (3,7) (4,7)}

D) {(2,7) (3,7) (4,7)}

Answer: D) {(2,7) (3,7) (4,7)}

31. The nth term of 1 + 3 + 5 + 7 + …..

A) 2n

B) 2n + 1

C) 2n – 1

D) 1 – 2n

Answer: C) 2n – 1

32. If x = 2.52 then ⌊52.2⌋ =

A) 0

B) 1

C) 2

D) 3

Answer: C) 2

33. The elements in level-1 are called ….…

A) electrons

B) atoms

C) neutrons

D) molecules

Answer: B) atoms

34. A Poset S is said to be ……. Set if for a, b in S exactly one of the conditions, a > b, a = b or b > a holds.

A) totally ordered

B) ordered

C) not ordered

D) completely ordered

Answer: A) totally ordered

35. Let (S,*) be a semigroup and let T be a subset of S. If T is closed under the operation *, Then (T,*) is called a …… of (S,*)

A) semigroup

B) supergroup

C) subgroup

D) subsemigroup

Answer: D) subsemigroup

36. The semigroup S/R is called the ……..

A) totally ordered

B) quotient semigroup

C) not ordered

D) completely ordered

Answer: B) quotient semigroup

37. A finite integral domain is a …….

A) subfield

B) vector

C) field

D) ring

Answer: C) field

38. An integral domain D is said to be of characteristic 0 if the relation ma ≠0 where 0≠a ∈ D and m is an integer, can hold only if

A) m = 0

B) m =1

C) m = 2

D) m = – 1

Answer: A) m = 0

39. P∧Q is called the ….… of P and Q.

A) conditional

B) conjunction

C) bi-conditional

D) disjunction

Answer: B) conjunction

40. In the implication P → Q, P is called the ……

A) consequent

B) premise

C) conditional

D) statement

Answer: B) premise

41. If A = {2, 3, 5} and B = {4, 6, 9} then if R is defined as R = {(a,b) ∈ bAxB/a} then the set R =

A) {(2,4), (2,6), (3,4), 3,9)}

B) {(2,4), (2,6), (3,6), 3,9)}

C) {(2,4), (2,9), (3,6), 3,9)}

D) {(4,2), (2,6), (3,6), 3,9)}

Answer: B) {(2,4), (2,6), (3,6), 3,9)}

42. If R = {(2,1), (3,1), (5,1), (5,4)} then R-1 =

A) {(2,1), (3,1), (5,1), (4,5)}

B) {(2,1), (3,1), (5,1), (5,4)}

C) {(1,2), (1,3), (1,5), (4,5)}

D) {(2,1), (3,1), (5,1), (4,5)}

Answer: C) {(1,2), (1,3), (1,5), (4,5)}

43. If 4th, 7th and 10th terms of G.P. are a, b, c respectively then

A) b2 = ac2

B) b2 = a+c

C) b2 = a2c2

D) b2 = ac

Answer: D) b2 = ac

44. A relation R on a set A is said to be symmetric if (a,b) ∈ R ⇒

A) (b,a) ∈ R

B) (b2,a2) ∈ R

C) (x,y) ∈ R

D) (y,x) Î R

Answer: A) (b,a) ∈ R

45. Consider the set of all straight lines in a plane. If the relation R is defined as “parallel to” then R is

A) reflexive

B) symmetric

C) transitive

D) A), B) and C)

Answer: D) A), B) and C)

46. The next permutation to 4123 in the reverse Lexicographic order is

A) 3412

B) 3421

C) 2413

D) 4312

Answer: C) 2413

47. Let (L, ∧, ∨) be an algebraic lattice and x∈L then x∧x =

A) x

B) x2

C) x3

D) 1/x

Answer: A) x

48. If L is a finite lattice then L is

A) supremum

B) infimum

C) bounded

D) unbounded

Answer: C) bounded

49. If H is a subgroup of G and a, b∈G. Then aH = bH if and only if

A) a-1 b-1 ∈ H

B) ab ∈ H

C) ab-1 ∈ H

D) a-1 b ∈ H

Answer: D) a-1 b ∈ H

50. If Φ is a homomorphism of G into G’ with kernel K then K is a …….. of G

A) normal subgroup

B) subgroup

C) bounded subgroup

D) unbounded subgroup

Answer: A) normal subgroup

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#### Conclusion

We hope that this quiz has helped you review some of the key concepts in discrete mathematics. If you’re looking for more practice, be sure to check out our other quizzes on counting and probability.

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