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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?
- Relation as a Matrix
- Relation as a Directed Graph
- Relation as an Arrow Diagram
- All of the above
Answer: D) All of the above
Explanation:
Relation can be represented in the following ways -
- Relation as a Matrix
- Relation as a Directed Graph
- Relation as an Arrow Diagram
2. How many types of relations are there?
- 6
- 7
- 8
- 9
Answer: D) 9
Explanation:
There are 9 types of relations.
3. Which of the following is/are the type(s) of relation?
- Reflexive relation
- Irreflexive relation
- Symmetric relation
- All of the above
Answer: D) All of the above
Explanation:
The following types of relations are there -
- Reflexive relation
- Irreflexive relation
- Symmetric relation
4. ____ for every a ∈ A is said to be a reflexive relation R on set A.
- (a, a) ∈ A
- (a) ∈ R
- (a, a) ∉ R
- (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.
- (a, a) ∈ A
- (a) ∈ R
- (a, a) ∉ R
- (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 ____.
- (a, b) ∈ R ⟺ (a) ∈ R
- (a, b) ∈ R ⟺ (b) ∈ R
- (a, b) ∈ R ⟺ (a, b) ∈ R
- (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.
- a = b
- a ≠ b
- a * b
- a - b
Answer: A) 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.
- Symmetric
- Antisymmetric
- Asymmetric
- None
Answer: C) Asymmetric
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 ____.
- Transitive
- Identity
- Void
- Universal
Answer: A) Transitive
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.
- Reflexive
- Transitive
- Symmetric
- All of the above
Answer: A) Reflexive
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).
- Identity
- Symmetric
- Void
- None
Answer: C) Void
Explanation:
The relation R: A → B is Void if R = ∅ (⊆ A x B).
12. Void relation has ____ properties, but it is not reflexive.
- Symmetrical
- Transitive
- Both A and B
- 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).
- Void
- Identity
- Universal
- Symmetric
Answer: C) Universal
Explanation:
The relation R: A → B is universal if R = A x B (⊆ A x B).
14. A → B's Universal Relationship is ____.
- Symmetrical
- Reflexive
- Transitive
- 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 ____.
- Equal relation
- Equivalence relation
- Symmetrical relation
- Asymptotic relation
Answer: B) Equivalence relation
Explanation:
If a relation is symmetrical, reflexive and transitive, then it is an equivalence relation.