# 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. 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
`[expand title="Show Answer"]C) Infinite set[/expand]`

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
`[expand title="Show Answer"]B) proper[/expand]`

3. Consider the set A = {1, 2, 3}, the power set of A has …. elements
A) 23
B) 22
C) 25
D) 26
`[expand title="Show Answer"]A) 23[/expand]`

4. The cardinality of the set A = {1, 2, 3, 0, 6, 7, 8, 9} is
A) 7
B) 8
C) 6
D) 2
`[expand title="Show Answer"]B) 8[/expand]`

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
`[expand title="Show Answer"]B) a + b / 2[/expand]`

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
`[expand title="Show Answer"]B) a + (n–1)d[/expand]`

7. The proposition ~p ν (p ν q) is a
A) Tautology
C) Logical equivalence
D) None of the above
`[expand title="Show Answer"]A) Tautology[/expand]`

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
`[expand title="Show Answer"]A) a / 1 – r[/expand]`

9. Combinatorics is the branch of discrete mathematics concerned with …..
A) counting problems
B) abstract algebra
C) derivative problems
D) integrated problems
`[expand title="Show Answer"]A) counting problems[/expand]`

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
`[expand title="Show Answer"]C) m + n[/expand]`

11. A relation means …… on a set S.
A) dual relation
B) binary relation
C) reflexive relation
D) symmetric relation
`[expand title="Show Answer"]B) binary relation[/expand]`

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
`[expand title="Show Answer"]D) Partially ordered set[/expand]`

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
`[expand title="Show Answer"]C) a covers b[/expand]`

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
`[expand title="Show Answer"]D) closure and associative law[/expand]`

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
`[expand title="Show Answer"]C) semigroup[/expand]`

16. The set Z with the binary operation “subtraction” is …… a subgroup
A) not
B) subset of
C) always
D) superset of
`[expand title="Show Answer"]A) not[/expand]`

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
`[expand title="Show Answer"]B) commutative ring[/expand]`

18. A commutative ring is said to be an integral domain if it has no …….
A) zero-divisors
B) inverse
C) multiples
D) identity
`[expand title="Show Answer"]A) zero-divisors[/expand]`

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
`[expand title="Show Answer"]C) Boolean ring[/expand]`

20. If R is a Boolean ring then R is a …….
A) commutative ring
B) subring
C) integral ring
D) integer
`[expand title="Show Answer"]A) commutative ring[/expand]`

21. Reasoning is a special kind of thinking called ….…
A) inferring
B) logics
C) bijective
`[expand title="Show Answer"]A) inferring[/expand]`

22. The basic unit of our objective language is called a …….
A) prime divisor
B) prime statement
C) bijective statement
D) statement
`[expand title="Show Answer"]B) prime statement[/expand]`

23. The validity of an argument does not guarantee the truth of the ……
A) permutation
B) commutative value
C) conclusion
D) identity value
`[expand title="Show Answer"]C) conclusion[/expand]`

24. A ……. is a statement that is either true or false, but not both.
A) argument
B) conclusion
C) bi-conditional
D) proposition
`[expand title="Show Answer"]D) proposition[/expand]`

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
`[expand title="Show Answer"]A) surjective[/expand]`

26. If f is onto then f(A) =
A) Φ
B) B
C) A
D) A x B
`[expand title="Show Answer"]B) B[/expand]`

27. The set {x ∈ R: a < x < b is denoted by
A) [a, b)
B) (a, b]
C) (a, b)
D) {a, b}
`[expand title="Show Answer"]C) (a, b)[/expand]`

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)
`[expand title="Show Answer"]D) f(x) = f(x + α)[/expand]`

29. f(x) = tanx is a periodic function with period …….
A) π
B) 2π
C) π/2
D) 3π
`[expand title="Show Answer"]A) π[/expand]`

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)}
`[expand title="Show Answer"]D) {(2,7) (3,7) (4,7)}[/expand]`

31. The nth term of 1 + 3 + 5 + 7 + …..
A) 2n
B) 2n + 1
C) 2n – 1
D) 1 – 2n
`[expand title="Show Answer"]C) 2n – 1[/expand]`

32. If x = 2.52 then ⌊52.2⌋ =
A) 0
B) 1
C) 2
D) 3
`[expand title="Show Answer"]C) 2[/expand]`

33. The elements in level-1 are called ….…
A) electrons
B) atoms
C) neutrons
D) molecules
`[expand title="Show Answer"]B) atoms[/expand]`

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
`[expand title="Show Answer"]A) totally ordered[/expand]`

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
`[expand title="Show Answer"]D) subsemigroup[/expand]`

36. The semigroup S/R is called the ……..
A) totally ordered
B) quotient semigroup
C) not ordered
D) completely ordered
`[expand title="Show Answer"]B) quotient semigroup[/expand]`

37. A finite integral domain is a …….
A) subfield
B) vector
C) field
D) ring
`[expand title="Show Answer"]C) field[/expand]`

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
`[expand title="Show Answer"]A) m = 0[/expand]`

39. P∧Q is called the ….… of P and Q.
A) conditional
B) conjunction
C) bi-conditional
D) disjunction
`[expand title="Show Answer"]B) conjunction[/expand]`

40. In the implication P → Q, P is called the ……
A) consequent
B) premise
C) conditional
D) statement
`[expand title="Show Answer"]B) premise[/expand]`

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)}
`[expand title="Show Answer"]B) {(2,4), (2,6), (3,6), 3,9)}[/expand]`

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)}
`[expand title="Show Answer"]C) {(1,2), (1,3), (1,5), (4,5)}[/expand]`

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
`[expand title="Show Answer"]D) b2 = ac[/expand]`

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
`[expand title="Show Answer"]A) (b,a) ∈ R[/expand]`

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)
`[expand title="Show Answer"]D) A), B) and C)[/expand]`

46. The next permutation to 4123 in the reverse Lexicographic order is
A) 3412
B) 3421
C) 2413
D) 4312
`[expand title="Show Answer"]C) 2413[/expand]`

47. Let (L, ∧, ∨) be an algebraic lattice and xL then x∧x =
A) x
B) x2
C) x3
D) 1/x
`[expand title="Show Answer"]A) x[/expand]`

48. If L is a finite lattice then L is
A) supremum
B) infimum
C) bounded
D) unbounded
`[expand title="Show Answer"]C) bounded[/expand]`

49. If H is a subgroup of G and a, bG. 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
`[expand title="Show Answer"]D) a-1 b ∈ H[/expand]`

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
`[expand title="Show Answer"]A) normal subgroup[/expand]`

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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.