This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Sets”.

1. A _______ is an ordered collection of objects.

a) Relation

b) Function

c) Set

d) Proposition

View Answer

Explanation: By the definition of set.

2. The set O of odd positive integers less than 10 can be expressed by ___________ .

a) {1, 2, 3}

b) {1, 3, 5, 7, 9}

c) {1, 2, 5, 9}

d) {1, 5, 7, 9, 11}

View Answer

Explanation: Odd numbers less than 10 is {1, 3, 5, 7, 9}.

3. Power set of empty set has exactly _____ subset.

a) One

b) Two

c) Zero

d) Three

View Answer

Explanation: Power set of null set has exactly one subset which is empty set.

a) {(1, a), (1, b), (2, a), (b, b)}

b) {(1, 1), (2, 2), (a, a), (b, b)}

c) {(1, a), (2, a), (1, b), (2, b)}

d) {(1, 1), (a, a), (2, a), (1, b)}

View Answer

Explanation: A subset R of the Cartesian product A x B is a relation from the set A to the set B.

5. The Cartesian Product B x A is equal to the Cartesian product A x B. Is it True or False?

a) True

b) False

View Answer

Explanation: Let A = {1, 2} and B = {a, b}. The Cartesian product A x B = {(1, a), (1, b), (2, a), (2, b)} and the Cartesian product B x A = {(a, 1), (a, 2), (b, 1), (b, 2)}. This is not equal to A x B.

6. What is the cardinality of the set of odd positive integers less than 10?

a) 10

b) 5

c) 3

d) 20

View Answer

Explanation: Set S of odd positive an odd integer less than 10 is {1, 3, 5, 7, 9}. Then, Cardinality of set S = |S| which is 5.

7. Which of the following two sets are equal?

a) A = {1, 2} and B = {1}

b) A = {1, 2} and B = {1, 2, 3}

c) A = {1, 2, 3} and B = {2, 1, 3}

d) A = {1, 2, 4} and B = {1, 2, 3}

View Answer

Explanation: Two set are equal if and only if they have the same elements.

a) Infinite

b) Finite

c) Subset

d) Empty

View Answer

Explanation: The set of positive integers is not finite.

9. What is the Cardinality of the Power set of the set {0, 1, 2}.

a) 8

b) 6

c) 7

d) 9

View Answer

Explanation: Power set P ({0, 1, 2}) is the set of all subsets of {0, 1, 2}. Hence,P({0, 1, 2}) = {null , {0}, {1}, {2}, {0, 1}, {0,2}, {1, 2}, {0, 1, 2}}.

10. The members of the set S = {x | x is the square of an integer and x < 100} is _________________.
a) {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}
b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
c) {1, 4, 9, 16, 25, 36, 64, 81, 85, 99}
d) {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}
[expand title="View Answer"] Answer: b
Explanation: The set S consists of the square of an integer less than 10.
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