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 2 of 5

Explore more Topics under Discrete Mathematics

01

Logics and Proofs

02

Sets and Functions

03

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04

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05

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06

Induction and Recursion

07

Counting Theory

08

Discrete Probability

09

Graphs and Graphs Properties

10

Tree Properties

11

Boolean Algebra and Modeling Computations

12

Group Theory

Q11.

R is a binary relation on a set S and R is reflexive if and only if _______

r(R) = R

s(R) = R

t(R) = R

f(R) = R

Discuss

Answer: (a).r(R) = R

Q12.

If R₁ and R₂ are binary relations from set A to set B, then the equality ______ holds.

(Rᶜ)ᶜ= Rᶜ

(A x B)ᶜ = Φ

(R₁ U R₂)ᶜ = R₁ᶜ∪ R₂ᶜ

(R₁ U R₂)ᶜ = R₁ᶜ ∩ R₂ᶜ

Discuss

Answer: (c).(R₁ U R₂)ᶜ = R₁ᶜ∪ R₂ᶜ

Q13.

The condition for a binary relation to be symmetric is _______

s(R) = R

R ∪ R = R

R = Rᶜ

f(R) = R

Discuss

Answer: (c).R = Rᶜ

Q14.

______ number of reflexive closure exists in a relation R = {(0,1), (1,1), (1,3), (2,1), (2,2), (3,0)} where {0, 1, 2, 3} ∈ A.

2⁶

Discuss

Answer: (b).6

Q15.

The transitive closure of the relation {(0,1), (1,2), (2,2), (3,4), (5,3), (5,4)} on the set {1, 2, 3, 4, 5} is _______

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

{(0,0), (1,1), (2,2), (3,3), (4,4), (5,5)}

{(0,1), (1,1), (2,2), (5,3), (5,4)}

{(0,1), (0,2), (1,2), (2,2), (3,4), (5,3), (5,4)}

Discuss

Answer: (d).{(0,1), (0,2), (1,2), (2,2), (3,4), (5,3), (5,4)}

Q16.

Amongst the properties {reflexivity, symmetry, antisymmetry, transitivity} the relation R={(a,b) ∈ N² | a!= b} satisfies _______ property.

symmetry

transitivity

antisymmetry

reflexivity

Discuss

Answer: (a).symmetry

Q17.

The number of equivalence relations of the set {3, 6, 9, 12, 18} is ______

2⁵

Discuss

Answer: (a).4

Q18.

Let R₁ and R₂ be two equivalence relations on a set. Is R₁ ∪ R₂ an equivalence relation?

an equivalence relation

reflexive closure of relation

not an equivalence relation

partial equivalence relation

Discuss

Answer: (a).an equivalence relation

Q19.

A relation R is defined on the set of integers as aRb if and only if a+b is even and R is termed as ______

an equivalence relation with one equivalence class

an equivalence relation with two equivalence classes

an equivalence relation

an equivalence relation with three equivalence classes

Discuss

Answer: (b).an equivalence relation with two equivalence classes

Q20.

The binary relation U = Φ (empty set) on a set A = {11, 23, 35} is _____

Neither reflexive nor symmetric

Symmetric and reflexive

Transitive and reflexive

Transitive and symmetric

Discuss

Answer: (d).Transitive and symmetric

Page 2 of 5

Welcome to the Relations MCQs Page

Relations MCQs | Page 2 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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