# Discrete Mathematics | Representation and Types of Relations MCQs

Discrete Mathematics | Representation and Types of Relations MCQs: This section contains multiple-choice questions and answers on Representation and Types of Relations in Discrete Mathematics.
Submitted by Anushree Goswami, on July 17, 2022

1. In which of the following ways can the relation be represented?

1. Relation as a Matrix
2. Relation as a Directed Graph
3. Relation as an Arrow Diagram
4. All of the above

Answer: D) All of the above

Explanation:

Relation can be represented in the following ways -

1. Relation as a Matrix
2. Relation as a Directed Graph
3. Relation as an Arrow Diagram

2. How many types of relations are there?

1. 6
2. 7
3. 8
4. 9

Explanation:

There are 9 types of relations.

3. Which of the following is/are the type(s) of relation?

1. Reflexive relation
2. Irreflexive relation
3. Symmetric relation
4. All of the above

Answer: D) All of the above

Explanation:

The following types of relations are there -

1. Reflexive relation
2. Irreflexive relation
3. Symmetric relation

4. ____ for every a ∈ A is said to be a reflexive relation R on set A.

1. (a, a) ∈ A
2. (a) ∈ R
3. (a, a) ∉ R
4. (a, a) ∈ R

Answer: D) (a, a) ∈ R

Explanation:

(a, a) ∈ R for every a ∈ A is said to be a reflexive relation R on set A.

5. ____ for every a ∈ A is said to be an irreflexive relation R on set A.

1. (a, a) ∈ A
2. (a) ∈ R
3. (a, a) ∉ R
4. (a, a) ∈ R

Answer: C) (a, a) ∉ R

Explanation:

(a, a) ∉ R for every a ∈ A is said to be a irreflexive relation R on set A.

6. Symmetric relations in set A are defined as ____.

1. (a, b) ∈ R ⟺ (a) ∈ R
2. (a, b) ∈ R ⟺ (b) ∈ R
3. (a, b) ∈ R ⟺ (a, b) ∈ R
4. (a, b) ∈ R ⟺ (b, a) ∈ R

Answer: D) (a, b) ∈ R ⟺ (b, a) ∈ R

Symmetric relations in set A are defined as (a, b) ∈ R ⟺ (b, a) ∈ R.

7. When (a, b) ∈ R and (b, a) ∈ R, then ____, a relation R is antisymmetric.

1. a = b
2. a ≠ b
3. a * b
4. a - b

Explanation:

When (a, b) ∈ R and (b, a) ∈ R, then a = b, a relation R is antisymmetric.

8. If for every (a, b) ∈ R, (b, a) does not belong to R, then R is an/the ____ relation.

1. Symmetric
2. Antisymmetric
3. Asymmetric
4. None

Explanation:

If for every (a, b) ∈ R, (b, a) does not belong to R, then R is an asymmetric relation.

9. When (a, b) ∈ R and (b, c) ∈ R ⟺ (a, c) ∈ R on set A, it is said that R is ____.

1. Transitive
2. Identity
3. Void
4. Universal

Explanation:

When (a, b) ∈ R and (b, c) ∈ R ⟺ (a, c) ∈ R on set A, it is said that R is transitive.

10. If set A is ____, then it is an identity relation.

1. Reflexive
2. Transitive
3. Symmetric
4. All of the above

Explanation:

If set A is reflexive, transitive and symmetric, then it is an identity relation.

11. The relation R: A → B is ____ if R = ∅ (⊆ A x B).

1. Identity
2. Symmetric
3. Void
4. None

Explanation:

The relation R: A → B is Void if R = ∅ (⊆ A x B).

12. Void relation has ____ properties, but it is not reflexive.

1. Symmetrical
2. Transitive
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

Void relation has symmetrical and transitive properties, but it is not reflexive.

13. The relation R: A → B is ____ if R = A x B (⊆ A x B).

1. Void
2. Identity
3. Universal
4. Symmetric

Explanation:

The relation R: A → B is universal if R = A x B (⊆ A x B).

14. A → B's Universal Relationship is ____.

1. Symmetrical
2. Reflexive
3. Transitive
4. All of the above

Answer: D) All of the above

Explanation:

A → B's Universal Relationship is symmetrical, reflexive, and transitive.

15. If a relation is symmetrical, reflexive and transitive, then it is a ____.

1. Equal relation
2. Equivalence relation
3. Symmetrical relation
4. Asymptotic relation

Explanation:

If a relation is symmetrical, reflexive and transitive, then it is an equivalence relation.