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 3 of 5

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Q21.

The binary relation {(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2)} on the set {1, 2, 3} is __________

reflective, symmetric and transitive

irreflexive, symmetric and transitive

neither reflective, nor irreflexive but transitive

irreflexive and antisymmetric

Discuss

Answer: (c).neither reflective, nor irreflexive but transitive

Q22.

Consider the relation: R’ (x, y) if and only if x, y>0 over the set of non-zero rational numbers,then R’ is _________

not equivalence relation

an equivalence relation

transitive and asymmetry relation

reflexive and antisymmetric relation

Discuss

Answer: (b).an equivalence relation

Q23.

Let S be a set of n>0 elements. Let be the number Bᵣ of binary relations on S and let Bf be the number of functions from S to S. The expression for Bᵣ and Bf, in terms of n should be ____________

n² and 2(n+1)²

n³ and n⁽ⁿ⁺¹⁾

n and n⁽ⁿ⁺⁶⁾

2⁽ⁿ*ⁿ⁾ and nⁿ

Discuss

Answer: (d).2⁽ⁿ*ⁿ⁾ and nⁿ

Q24.

Let A be a set of k (k>0) elements. Which is larger between the number of binary relations (say, Nr) on A and the number of functions (say, Nf) from A to A?

number of relations

number of functions

the element set

number of subsets of the relation

Discuss

Answer: (a).number of relations

Q25.

Consider the binary relation, A = {(a,b) | b = a – 1 and a, b belong to {1, 2, 3}}. The reflexive transitive closure of A is?

{(a,b) | a >= b and a, b belong to {1, 2, 3}}

{(a,b) | a > b and a, b belong to {1, 2, 3}}

{(a,b) | a <= b and a, b belong to {1, 2, 3}}

{(a,b) | a = b and a, b belong to {1, 2, 3}}

Discuss

Answer: (a).{(a,b) | a >= b and a, b belong to {1, 2, 3}}

Q26.

Let R₁ be a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} and R₂ be another relation from B to C = {1, 2, 3, 4} as defined below:

i. An element a in A is related to an element b in B (under R₁) if a * b is divisible by 3.

ii. An element a in B is related to an element b in C (under R₂) if a * b is even but not divisible by 3. Which is the composite relation R₁R₂ from A to C?

R₁R₂ = {(1, 2), (1, 4), (3, 3), (5, 4), (5,6), (7, 3)}

R₁R₂ = {(1, 2), (1,6), (3, 2), (3, 4), (5, 4), (7, 2)}

R₁R₂ = {(2,2), (3, 2), (3, 4), (5, 1), (5, 3), (7, 1)}

Discuss

Answer: (b).Φ

Q27.

The time complexity of computing the transitive closure of a binary relation on a set of n elements should be ________

O(n)

O(logn)

O(n⁽ⁿ⁺⁽³/²⁾⁾)

O(n3)

Discuss

Answer: (b).O(n³)

Q28.

Let A and B be two non-empty relations on a set S. Which of the following statements is false?

A and B are transitive ⇒ A∩B is transitive

A and B are symmetric ⇒ A∪B is symmetric

A and B are transitive ⇒ A∪B is not transitive

A and B are reflexive ⇒ A∩B is reflexive

Discuss

Answer: (c).A and B are transitive ⇒ A∪B is not transitive

Q29.

Determine the characteristics of the relation aRb if a² = b².

Transitive and symmetric

Reflexive and asymmetry

Trichotomy, antisymmetry, and irreflexive

Symmetric, Reflexive, and transitive

Discuss

Answer: (d).Symmetric, Reflexive, and transitive

Q30.

Let R be a relation between A and B. R is asymmetric if and only if ________

Intersection of D(A) and R is empty, where D(A) represents diagonal of set

R⁻¹ is a subset of R, where R⁻¹ represents inverse of R

Intersection of R and R⁻¹ is D(A)

D(A) is a subset of R, where D(A) represents diagonal of set

Discuss

Answer: (a).Intersection of D(A) and R is empty, where D(A) represents diagonal of set

Page 3 of 5

Welcome to the Relations MCQs Page

Relations MCQs | Page 3 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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