Relation R = {(1, 2), (2, 3), (1, 3)} is a/an1. Reflexive2. Transitiv

1.	Relation R = {(1, 2), (2, 3), (1, 3)} is a/an1. Reflexive2. Transitive3. Symmetric4. None of these
Answer» Correct Answer - Option 2 : Transitive Concept: A relation R in a set A is called Reflexive, if (a, a) ∈ R, for every a ∈ A. Symmetric, if (a, b) ∈ R implies that (b, a) ∈ R, for all a, b ∈A. Transitive, if (a, b) ∈ R and (b, c) ∈ R implies that (a, c) ∈ R, for all a, b, c ∈A. Calculation: Given: R = {(1, 2), (2, 3), (1, 3)} Reflexive: As we can see that, (1, 1), (2, 2) does not belong to R. Hence R is not reflexive. Symmetric: As we can see that, (1, 2) ∈ R but (2, 1) does not belong to R. Hence relation R is not symmetric. Transitive: As we can see that (1, 2), (2, 3)∈ R and (1, 3) also belong to R. Hence relation R is transitive. Hence, option 2 is the correct answer.

Relation R = {(1, 2), (2, 3), (1, 3)} is a/an1. Reflexive2. Transitive3. Symmetric4. None of these

Answer» Correct Answer - Option 2 : Transitive

Concept:

A relation R in a set A is called

Reflexive, if (a, a) ∈ R, for every a ∈ A.
Symmetric, if (a, b) ∈ R implies that (b, a) ∈ R, for all a, b ∈A.
Transitive, if (a, b) ∈ R and (b, c) ∈ R implies that (a, c) ∈ R, for all a, b, c ∈A.

Calculation:

Given: R = {(1, 2), (2, 3), (1, 3)}

Reflexive:

As we can see that, (1, 1), (2, 2) does not belong to R. Hence R is not reflexive.

Symmetric:

As we can see that, (1, 2) ∈ R but (2, 1) does not belong to R. Hence relation R is not symmetric.

Transitive:

As we can see that (1, 2), (2, 3)∈ R and (1, 3) also belong to R. Hence relation R is transitive.

Hence, option 2 is the correct answer.

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Relation R = {(1, 2), (2, 3), (1, 3)} is a/an1. Reflexive2. Transitive3. Symmetric4. None of these

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