Welcome to the Relations MCQs Page

Dive deep into the fascinating world of Relations with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Relations, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Relations, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Discrete Mathematics.

Check out the MCQs below to embark on an enriching journey through Relations. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Relations. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Relations MCQs | Page 5 of 5

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Q41.

Suppose a relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)} on S = {3, 5, 6}. Here R is known as _________

equivalence relation

reflexive relation

symmetric relation

transitive relation

Discuss

Answer: (a).equivalence relation

Q42.

Consider the congruence 45≡3(mod 7). Find the set of equivalence class representatives.

{…, 0, 7, 14, 28, …}

{…, -3, 0, 6, 21, …}

{…, 0, 4, 8, 16, …}

{…, 3, 8, 15, 21, …}

Discuss

Answer: (a).{…, 0, 7, 14, 28, …}

Q43.

Which of the following relations is the reflexive relation over the set {1, 2, 3, 4}?

{(0,0), (1,1), (2,2), (2,3)}

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

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

{(0,1), (1,1), (2,3), (2,2), (3,4), (3,1)

Discuss

Answer: (b).{(1,1), (1,2), (2,2), (3,3), (4,3), (4,4)}

Q44.

Determine the partitions of the set {3, 4, 5, 6, 7} from the following subsets.

{3,5}, {3,6,7}, {4,5,6}

{3}, {4,6}, {5}, {7}

{3,4,6}, {7}

{5,6}, {5,7}

Discuss

Answer: (b).{3}, {4,6}, {5}, {7}

Q45.

Determine the number of equivalence classes that can be described by the set {2, 4, 5}.

125

Discuss

Answer: (b).5

Q46.

Determine the number of possible relations in an antisymmetric set with 19 elements.

23585

2.02 * 10⁸⁷

9.34 * 7⁹¹

35893

Discuss

Answer: (b).2.02 * 10⁸⁷

Q47.

For a, b ∈ Z deﬁne a | b to mean that a divides b is a relation which does not satisfy ___________

irreflexive and symmetric relation

reflexive relation and symmetric relation

transitive relation

symmetric relation

Discuss

Answer: (b).reflexive relation and symmetric relation

Q48.

Which of the following is an equivalence relation on R, for a, b ∈ Z?

(a-b) ∈ Z

(a²+c) ∈ Z

(ab+cd)/2 ∈ Z

(2c³)/3 ∈ Z

Discuss

Answer: (b).(a²+c) ∈ Z

Q49.

Determine the set of all integers a such that a ≡ 3 (mod 7) such that −21 ≤ x ≤ 21.

{−21, −18, −11, −4, 3, 10, 16}

{−21, −18, −11, −4, 3, 10, 17, 24}

{−24, -19, -15, 5, 0, 6, 10}

{−23, −17, −11, 0, 2, 8, 16}

Discuss

Answer: (b).{−21, −18, −11, −4, 3, 10, 17, 24}

Q50.

For a, b ∈ R deﬁne a = b to mean that |x| = |y|. If [x] is an equivalence relation in R. Find the equivalence relation for [17].

{,…,-11, -7, 0, 7, 11,…}

{2, 4, 9, 11, 15,…}

{-17, 17}

{5, 25, 125,…}

Discuss

Answer: (c).{-17, 17}

Page 5 of 5

Welcome to the Relations MCQs Page

Relations MCQs | Page 5 of 5

Explore more Topics under Discrete Mathematics

Logics and Proofs

Sets and Functions

Sequences,Sums and Matrices

Algorithms

Number Theory and Cryptography

Induction and Recursion

Counting Theory

Discrete Probability

Graphs and Graphs Properties

Tree Properties

Boolean Algebra and Modeling Computations

Group Theory

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