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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 2 of 5

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Q11.
R is a binary relation on a set S and R is reflexive if and only if _______

a.

r(R) = R

b.

s(R) = R

c.

t(R) = R

d.

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.

a.

(Rᶜ)ᶜ= Rᶜ

b.

(A x B)ᶜ = Φ

c.

(R₁ U R₂)ᶜ = R₁ᶜ∪ R₂ᶜ

d.

(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 _______

a.

s(R) = R

b.

R ∪ R = R

c.

R = Rᶜ

d.

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.

a.

2⁶

b.

6

c.

8

d.

36

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 _______

a.

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

b.

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

c.

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

d.

{(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.

a.

symmetry

b.

transitivity

c.

antisymmetry

d.

reflexivity

Discuss
Answer: (a).symmetry
Q17.
The number of equivalence relations of the set {3, 6, 9, 12, 18} is ______

a.

4

b.

2⁵

c.

22

d.

90

Discuss
Answer: (a).4
Q18.
Let R₁ and R₂ be two equivalence relations on a set. Is R₁ ∪ R₂ an equivalence relation?

a.

an equivalence relation

b.

reflexive closure of relation

c.

not an equivalence relation

d.

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 ______

a.

an equivalence relation with one equivalence class

b.

an equivalence relation with two equivalence classes

c.

an equivalence relation

d.

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 _____

a.

Neither reflexive nor symmetric

b.

Symmetric and reflexive

c.

Transitive and reflexive

d.

Transitive and symmetric

Discuss
Answer: (d).Transitive and symmetric
Page 2 of 5

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