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Discrete Mathematics MCQ Questions with Answers is a pdf document containing 50 questions and answers covering various topics in Discrete Mathematics.
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Discrete Mathematics MCQ Quiz with Answers
1) If a set A has n elements then its power set P((A) has ___ elements.
(a) 2n
(b) 2n
(c) 2+n
(d) 2-n
Answer: (b) 2n
2) Difference between two sets A & B i.e. A-B is the set of elements of ___.
(a) A which are in B
(b) B which are not in A
(c) A which are not in B
(d) None of the above
Answer: (c) A which is not in B
3) For any three sets A, B, C, A – (BU(C) =
(a) (A-(B) U (A-(C)
(b) A – (B∩(C)
(c) (A – (B) UC
(d) (A-(B) ∩ (A-(C)
Answer: (d) (A-(B) ∩ (A-(C)
4) R = {(2, 4), (2, 6), (3, 6), (3, 9)} domain of R is-
(a) {2, 3}
(b) {4, 6, 9}
(c) {2, 3, 4, 6, 9}
(d) None of the above
Answer: (a) {2, 3}
5) If a relation R in a set A is distributive if (a, (b) ÎR, (b,(c) ÎR it implies
(a) (a, (b) Î R
(b) (b, (c) Î R
(c) (a, (c) ÎR
(d) (c, (a) ÎR
Answer: (c) (a, (c) ÎR
6) R is an equivalence relation if-
(a) R is reflexive
(b) R is symmetric
(c) R is transitive
(d) All of the above
Answer: (d) All of the above
7) Which of the following is an open interval?
(a) [a, b)
(b) [a, b]
(c) (a, b)
(d) None of the above
Answer: (b) [a, b]
8) Value of p (n, r) is –
(a) n!/r! (n-r) !
(b) r!/(n-r) !
(c) n!/(n-r)!
(d) (n-r) !/n!
Answer: (c) n!/(n-r)!
9) Value of ë99.1û is
(a) 99
(b) 98
(c) 100
(d) 99.1
Answer: (a) 99
10) Glb of S1
(a) {1, 2}
(b) {3, 4, 5}
(c) {3, 4, 5, 6, 7, 8}
(d) None
Answer: (d) None
11) Lub of S2
(a) {1, 2}
(b) {6, 7, 8}
(c) {3}
(d) None
Answer: (d) None
12) Lower bound of S1.
(a) {1, 2}
(b) {1, 2, 3, 4}
(c) {4, 5, 6}
(d) None
Answer: (d) None
13) Glb of S2.
(a) {1, 2}
(b) 3
(c) {4, 5, 6, 7, 8}
(d) None
Answer: (b) 3
14) Lub of S1
(a) {1, 2}
(b) {1, 2, 3, 4}
(c) {4, 5, 6}
(d) None
Answer: (d) None
15) Upper bound of S1
(a) 3,4,5,6,7,8
(b) 1,2,3
(c) 6,7,8,
(d) None
Answer: (a) 3,4,5,6,7,8
16) Upper bound of S2
(a) 3,4,5,6,7,8
(b) 1,2,3
(c) 6,7,8
(d) None
Answer: (c) 6,7,8
17) (A, *) be an algebraic system whereas is the binary operation on A (A, *) is called a semi-group if-
(a) * is a closed operation
(b) * is an associative operation
(c) None of the above
(d) All of the above
Answer: (d) All of the above
18) (A, *) be an algebraic system where * is a binary operation on A. (A, *) is called monoid if it satisfies.
(a) * is a closed operation
(b) * is an associative operation
(c) Existence of identity
(d) All of the above
Answer: (d) All of the above
19) A nonempty set G together with a binary operation * is called a group if the algebraic system (G, *) satisfies.
(a) (a, (b) are elements of G, which implies (a*(b) is an element of G
(b) (a*(b)*c = a* (b*(c) for all a, b, c Є G
(c) There exists are element e in G such that a*e =e*a= a for all a Є G
(d) For any element a m G there corresponds an element b in G such that a * b = b *a
(e) All of the above
Answer: (e) All of the above
20) Which of the following is not a proportion?
(a) Bangalore is the capital city of Karnataka.
(b) 3+6=7
(c) x+y+5=9
(d) Berlin is the capital of Australia
Answer: (c) x+y+5=9
21) The laptop is not good but cheap.
(a) p ۸ q
(b) (~p) ۸ q
(c) (~ p) ۸ (~q)
(d) (p۷q)
Answer: (b) (~p) ۸ q
22) This laptop is neither good nor cheap.
(a) (p ۷ q)
(b) p ۸ q
(c) ~ p ۸ ~q
(d) p ۷ q
Answer: (c) ~ p ۸ ~q
23) The predicate in the statement. Stefan is a Mathematician
(a) Stephen
(b) is a
(c) Stephen is a
(d) Is a mathematician
Answer: (d) Is a mathematician
24) Bhanu is taller than Prajwal.
(a) Bhanu
(b) Prajwal
(c) is taller than
(d) taller than Prajwal
Answer: (c) is taller than
25) P(x) = x>3. P(2) = ? Truth value
(a) F
(b) T
(c) Either F & T
(d) Neither F nor T
Answer: (a) F
26) Write ~p if p is – x>20
(a) x=20
(b) x<20
(c) x!=20
(d) None of the above
Answer: (b) x<20
27) p ↔ q means-
(a) p → q & q → p
(b) p ۸ p & q → p
(c) p ۸ q, q ۸ p
(d) p → q, q → p
Answer: (a) p → q & q → p
28) ~ (p ۷ q) means =
(a) (p) ۷ (q)
(b) (p) ۸ (q)
(c) (~p) ۸ (~q)
(d) (p) ۸ (q)
Answer: (c) (~p) ۸ (~q)
29) Which of the following is not wff
(a) (p ۸ q)
(b) (p → (p ۷ Q)
(c) (p ۸ Q) → Q
(d) (p ۷ Q)
Answer: (c) (p ۸ Q) → Q
30) Which of the following is wff
(a) (p ۸ Q) → Q
(b) (p → Q) → (۸ Q)
(c) (p → (Q → R)
(d) p → Q
Answer: (c) (p → (Q → R)
31) (a+(b)2 = ? if a, b Є R
(a) a2 + b2 + 2ab
(b) a2 – b2 + 2ab
(c) a2 + ab + ba + b2
(d) a2 + ab + ba – b2
Answer: (d) a2 + ab + ba – b2
32) If A = { 2, 3, 4 }, B = { 4, 5, 6 }, C = { 6, 7 } then (A-(B) * (B-(C) =
(a) { (2, 7), (3, 7), (4, 7) }
(b) { (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5) }
(c) { (2, 4), (2, 5), (3, 4), (3, 5) }
(d) { (4, 4), (4, 5) }
Answer: (c) { (2, 4), (2, 5), (3, 4), (3, 5) }
33) The domain & range of function F(x) = X/1+X2
(a) N, [-1/2, 0) U (0, ½]
(b) R, [-1/2, 0) U (0, ½]
(c) R, [-1/2, 0] U [0, 1/2]
(d) R, (-1/2, 0) U (0, ½)
Answer: (b) R, [-1/2, 0) U (0, ½]
34) Range of sin function-
(a) [-1, +1)
(b) (-1, 0)
(c) [-1, +1]
(d) (0, -1)
Answer: (a) [-1, +1)
35) Nth term of the series -1 + ½ + ¼ +1/8
(a) 2n -1
(b) 1/2n-1
(c) 1/2n -1
(d) 2n-1
Answer: (c) 1/2n -1
36) Sum of all four-digit no. that can be obtained by using the digits 1, 2, 3, 4 once in each.
(a) 66,660
(b) 70,660
(c) 66,670
(d) 66,666
Answer: (a) 66,660
37) Solve an=3an-1 x>1, ao =1
(a) 3n
(b) 3n
(c) 3+n
(d) 3-n
Answer: (b) 3n
38) [p۸ (p۸q)] ۷p is-
(a) Tautology
(b) Proposition
(c) Contradiction
(d) Statement
Answer: (a) Tautology
39) Consider the following statement some men are clever is written as –
(a) ($ x) (m (x))
(b) (x (m (x) ۸ (C (x))
(c) (x) (m(x)) ۷ ((x)
(d) (” x) (m(x) ۸ ((x)
Answer: (b) (x (m (x) ۸ (C (x))
40) Some real numbers are rational.
(a) (” x) ((R (x) ۸ (x))
(b) (x) (R(x)
(c) (x) (R(x) (x))
(d) (x) (R(x) ۸ (x))
Answer: (d) (x) (R(x) ۸ (x))
41) Convert the following statements into symbolic logic. All beautiful birds are ornately colored
(a) (x) ((D(x) ۷ B(x) → O(x))
(b) (x) ((D(x) ۸ B(x) → O(x))
(c) (x) ((D(x) ۸ B(x) ↔ O(x))
(d) (x) ((D(x) ۸ B(x) → O(x))
Answer: (b) (x) ((D(x) ۸ B(x) → O(x))
42) Birds that do not live on honey are dull in color.
(a) (x) ((D(x) ۷ H(x) → O(x))
(b) (x) ((D(x) ۸ H(x) → O(x))
(c) (x) ((D(x) ۸ H(x) → O(x))
(d) (x) ((D(x) ۸ H(x) ↔ O(x))
Answer: (b) (x) ((D(x) ۸ H(x) → O(x))
43) Determine which of the following are in partial order?
(a) R1 = {(a, (b) Є z * z / a-b ≤ 1 } on z
(b) R2 = {(a, (b) Є z * z / ((a) ≤ b } on z
(c) R3 = {(a, (b) Є z * z / a divides b in z} on z
(d) R4 = {(a, (b) Є z *z / a-b ≤ 0}
Answer: (d) R4 = {(a, (b) Є z *z / a-b ≤ 0}
44) (A, *) be an algebraic system where * is a binary operation on A (A, *) is called a semigroup if it satisfies.
(a) * is a closed operation i.e. a*b Є A for all a, b Є A
(b) * is an associative operation i.e. a* (b*(c) = (a*(b) * c for all a, b, c Є A
(c) All of the above
(d) None of the above
Answer: (c) All of the above
45) If f(x) = x2 +3 and g(x) = 4x -5; then g of is
(a) 1
(b) 4×2 + 3
(c) -5
(d) None
Answer: (d) None
46) F(x) = 1/1-X, X ≠ 1 , F [F{F(X)}] = ?
(a) X2
(b) X/X-1
(c) X-1/X
(d) X
Answer: (d) X
47) If Tp = q, Tq = p than Tp+q = ?
(a) 0
(b) p+q
(c) p
(d) q
Answer: (a) 0
48) Using mathematical induction solution of the series. 13 + 23 + 33 + ___ + x3
(a) n2 (n+1)2/2
(b) n3 (n2+n+1)/3
(c) n2 (n+1)2/4
(d) n(n+1)/2
Answer: (b) n3 (n2+n+1)/3
49) Sum of n bracket series is (1) + (1+2) + (1+2+3) ___
(a) n(n+1) (x+2) (x+3)/127
(b) n(n+1) (x+2)/4
(c) n(n+1)/2
(d) n(n+1) (n+2)/6
Answer: (d) n(n+1) (n+2)/6
50) Sum of to infinity the series. 1 + 4/9 + 7/92 + 10/93 + ___
(a) 99/66
(b) 77/64
(c) 99/81
(d) 99/64
Answer: (a) 99/66
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Conclusion
These questions and answers should help you review the basic concepts of discrete mathematics. If you’re still having trouble understanding some of the material, be sure to consult your textbook or a tutor.
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