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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.

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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 _________

a.

equivalence relation

b.

reflexive relation

c.

symmetric relation

d.

transitive relation

Discuss
Answer: (a).equivalence relation
Q42.
Consider the congruence 45≡3(mod 7). Find the set of equivalence class representatives.

a.

{…, 0, 7, 14, 28, …}

b.

{…, -3, 0, 6, 21, …}

c.

{…, 0, 4, 8, 16, …}

d.

{…, 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}?

a.

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

b.

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

c.

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

d.

{(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.

a.

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

b.

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

c.

{3,4,6}, {7}

d.

{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}.

a.

125

b.

5

c.

16

d.

72

Discuss
Answer: (b).5
Q46.
Determine the number of possible relations in an antisymmetric set with 19 elements.

a.

23585

b.

2.02 * 10⁸⁷

c.

9.34 * 7⁹¹

d.

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 ___________

a.

irreflexive and symmetric relation

b.

reflexive relation and symmetric relation

c.

transitive relation

d.

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.

(a-b) ∈ Z

b.

(a²+c) ∈ Z

c.

(ab+cd)/2 ∈ Z

d.

(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.

a.

{−21, −18, −11, −4, 3, 10, 16}

b.

{−21, −18, −11, −4, 3, 10, 17, 24}

c.

{−24, -19, -15, 5, 0, 6, 10}

d.

{−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].

a.

{,…,-11, -7, 0, 7, 11,…}

b.

{2, 4, 9, 11, 15,…}

c.

{-17, 17}

d.

{5, 25, 125,…}

Discuss
Answer: (c).{-17, 17}
Page 5 of 5

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