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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.

The questions are divided into different categories such as Basic Concepts, Algebra, Probability, etc. The answers are concise and to the point, making it an ideal resource for students looking for practice material or clarification on specific concepts.

In this MCQ Quiz article, we will provide you with a list of Discrete Mathematics MCQ questions with answers that can help you in your learning process. So don’t wait any longer and start studying!

#### Brief About Discrete Mathematics

Discrete Mathematics is the study of mathematics that deals with discrete objects, such as numbers, symbols, and mathematical expressions. Discrete Math can be used to solve problems that cannot be solved using algebra or other more general methods.

For example, solving a system of linear equations can be solved using Discrete Math techniques, but solving a system of nonlinear equations may not be possible using only those techniques.

## 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) 2^{n
}(c) 2+n

(d) 2-n

`[expand title="Show Answer"](b) 2n[/expand]`

`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

`[expand title="Show Answer"](c) A which is not in B[/expand]`

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)

`[expand title="Show Answer"](d) (A-(B) ∩ (A-(C)[/expand]`

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

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

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

`[expand title="Show Answer"](c) (a, (c) ÎR[/expand]`

6) R is an equivalence relation if-

(a) R is reflexive

(b) R is symmetric

(c) R is transitive

(d) All of the above

`[expand title="Show Answer"](d) All of the above[/expand]`

7) Which of the following is an open interval?

(a) [a, b)

(b) [a, b]

(c) (a, b)

(d) None of the above

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

8) Value of p (n, r) is –

(a) n!/r! (n-r) !

(b) r!/(n-r) !

(c) n!/(n-r)!

(d) (n-r) !/n!

`[expand title="Show Answer"](c) n!/(n-r)![/expand]`

9) Value of ë99.1û is

(a) 99

(b) 98

(c) 100

(d) 99.1

`[expand title="Show Answer"](a) 99[/expand]`

10) Glb of S1

(a) {1, 2}

(b) {3, 4, 5}

(c) {3, 4, 5, 6, 7, 8}

(d) None

`[expand title="Show Answer"](d) None[/expand]`

11) Lub of S2

(a) {1, 2}

(b) {6, 7, 8}

(c) {3}

(d) None

`[expand title="Show Answer"](d) None[/expand]`

12) Lower bound of S1.

(a) {1, 2}

(b) {1, 2, 3, 4}

(c) {4, 5, 6}

(d) None

`[expand title="Show Answer"](d) None[/expand]`

13) Glb of S2.

(a) {1, 2}

(b) 3

(c) {4, 5, 6, 7, 8}

(d) None

`[expand title="Show Answer"](b) 3[/expand]`

14) Lub of S1

(a) {1, 2}

(b) {1, 2, 3, 4}

(c) {4, 5, 6}

(d) None

`[expand title="Show Answer"](d) None[/expand]`

15) Upper bound of S1

(a) 3,4,5,6,7,8

(b) 1,2,3

(c) 6,7,8,

(d) None

`[expand title="Show Answer"](a) 3,4,5,6,7,8[/expand]`

16) Upper bound of S2

(a) 3,4,5,6,7,8

(b) 1,2,3

(c) 6,7,8

(d) None

`[expand title="Show Answer"](c) 6,7,8[/expand]`

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

`[expand title="Show Answer"](d) All of the above[/expand]`

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

`[expand title="Show Answer"](d) All of the above[/expand]`

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

`[expand title="Show Answer"](e) All of the above[/expand]`

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

`[expand title="Show Answer"](c) x+y+5=9[/expand]`

21) The laptop is not good but cheap.

(a) p ۸ q

(b) (~p) ۸ q

(c) (~ p) ۸ (~q)

(d) (p۷q)

`[expand title="Show Answer"](b) (~p) ۸ q[/expand]`

22) This laptop is neither good nor cheap.

(a) (p ۷ q)

(b) p ۸ q

(c) ~ p ۸ ~q

(d) p ۷ q

`[expand title="Show Answer"](c) ~ p ۸ ~q[/expand]`

23) The predicate in the statement. Stefan is a Mathematician

(a) Stephen

(b) is a

(c) Stephen is a

(d) Is a mathematician

`[expand title="Show Answer"](d) Is a mathematician[/expand]`

24) Bhanu is taller than Prajwal.

(a) Bhanu

(b) Prajwal

(c) is taller than

(d) taller than Prajwal

`[expand title="Show Answer"](c) is taller than[/expand]`

25) P(x) = x>3. P(2) = ? Truth value

(a) F

(b) T

(c) Either F & T

(d) Neither F nor T

`[expand title="Show Answer"](a) F[/expand]`

26) Write ~p if p is – x>20

(a) x=20

(b) x<20

(c) x!=20

(d) None of the above

`[expand title="Show Answer"](b) x<20[/expand]`

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

`[expand title="Show Answer"](a) p → q & q → p[/expand]`

28) ~ (p ۷ q) means =

(a) (p) ۷ (q)

(b) (p) ۸ (q)

(c) (~p) ۸ (~q)

(d) (p) ۸ (q)

`[expand title="Show Answer"](c) (~p) ۸ (~q)[/expand]`

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)

`[expand title="Show Answer"](c) (p ۸ Q) → Q[/expand]`

30) Which of the following is wff

(a) (p ۸ Q) → Q

(b) (p → Q) → (۸ Q)

(c) (p → (Q → R)

(d) p → Q

`[expand title="Show Answer"](c) (p → (Q → R)[/expand]`

31) (a+(b)^{2} = ? if a, b Є R

(a) a^{2} + b^{2} + 2ab

(b) a^{2} – b^{2} + 2ab

(c) a^{2} + ab + ba + b^{2}

(d) a^{2} + ab + ba – b^{2
}`[expand title="Show Answer"](d) a2 + ab + ba – b2[/expand]`

^{
}

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) }

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

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)

`[expand title="Show Answer"](b) R, [-1/2, 0) U (0, ½][/expand]`

34) Range of sin function-

(a) [-1, +1)

(b) (-1, 0)

(c) [-1, +1]

(d) (0, -1)

`[expand title="Show Answer"](a) [-1, +1)[/expand]`

35) Nth term of the series -1 + ½ + ¼ +1/8

(a) 2^{n -1
}(b) 1/2^{n-1
}(c) 1/2^{n -1
}(d) 2^{n-1
}`[expand title="Show Answer"](c) 1/2n -1[/expand]`

^{
}

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

`[expand title="Show Answer"](a) 66,660[/expand]`

37) Solve a_{n}=3a_{n-1} x>1, a_{o} =1

(a) 3n

(b) 3n

(c) 3+n

(d) 3-n

`[expand title="Show Answer"](b) 3n[/expand]`

38) [p۸ (p۸q)] ۷p is-

(a) Tautology

(b) Proposition

(c) Contradiction

(d) Statement

`[expand title="Show Answer"](a) Tautology[/expand]`

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)

`[expand title="Show Answer"](b) (x (m (x) ۸ (C (x))[/expand]`

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))

`[expand title="Show Answer"](d) (x) (R(x) ۸ (x))[/expand]`

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))

`[expand title="Show Answer"](b) (x) ((D(x) ۸ B(x) → O(x))[/expand]`

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))

`[expand title="Show Answer"](b) (x) ((D(x) ۸ H(x) → O(x))[/expand]`

43) Determine which of the following are in partial order?

(a) R_{1} = {(a, (b) Є z * z / a-b ≤ 1 } on z

(b) R_{2} = {(a, (b) Є z * z / ((a) ≤ b } on z

(c) R_{3} = {(a, (b) Є z * z / a divides b in z} on z

(d) R_{4} = {(a, (b) Є z *z / a-b ≤ 0}

`[expand title="Show Answer"](d) R`

_{4} = {(a, (b) Є z *z / a-b ≤ 0}[/expand]

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

`[expand title="Show Answer"](c) All of the above[/expand]`

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

`[expand title="Show Answer"](d) None[/expand]`

46) F(x) = 1/1-X, X ≠ 1 , F [F{F(X)}] = ?

(a) X^{2
}(b) X/X-1

(c) X-1/X

(d) X

`[expand title="Show Answer"](d) X[/expand]`

47) If Tp = q, Tq = p than Tp+q = ?

(a) 0

(b) p+q

(c) p

(d) q

`[expand title="Show Answer"](a) 0[/expand]`

48) Using mathematical induction solution of the series. 1^{3} + 2^{3} + 3^{3} + ___ + x^{3
}(a) n^{2} (n+1)^{2}/2

(b) n^{3} (n^{2}+n+1)/3

(c) n^{2} (n+1)^{2}/4

(d) n(n+1)/2

`[expand title="Show Answer"](b) n`

^{3} (n^{2}+n+1)/3[/expand]

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

`[expand title="Show Answer"](d) n(n+1) (n+2)/6[/expand]`

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

`[expand title="Show Answer"](a) 99/66[/expand]`

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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.

With a little practice, you’ll be able to solve these problems like a pro!

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