Let A = {3, 4, 5} and relation R = {(a, b): a, b ∈ A, a divides b a

1.	Let A = {3, 4, 5} and relation R = {(a, b): a, b ∈ A, a divides b and b divides a} then relation R-1 is1. Identity relation2. Universal relation3. both a and b4. empty relation
Answer» Correct Answer - Option 1 : Identity relation Concept: If R is a relation from set A to set B, then inverse relation of R to be denoted by R-1, is a relation from set B to set A. Symbolically R-1 = {(b, a): (a, b) ∈ R for all a ∈ A and b ∈ B}. A relation R on a set A is said to be identity relation on A if R = {(a, b): a ∈ A, b ∈ A and a = b}. A relation R from A to B is said to be the universal relation, if R = A × B. A relation R from A to B is called an empty relation or a void relation from A to B if R = ø. Calculation: A = {3, 4, 5} Cartesian product \(A× A\) = {(3, 3), (3, 4), (3, 5), (4, 3), (4, 4),(4, 5), (5, 3), (5, 4), (5, 5)} Given, R = {(a, b): a, b ∈ A, a divides b and b divides a} R^-1 = {(b, a): a, b ∈ A, b divides a and a divides b} If b divides a and a divides b. it is only possible if a = b. Hence, relation R^-1 = {(3, 3), (4, 4), (5, 5)}. therefore R^-1 is an identity relation.

Let A = {3, 4, 5} and relation R = {(a, b): a, b ∈ A, a divides b and b divides a} then relation R-1 is1. Identity relation2. Universal relation3. both a and b4. empty relation

Answer» Correct Answer - Option 1 : Identity relation

Concept:

If R is a relation from set A to set B, then inverse relation of R to be denoted by R-1, is a relation from set B to set A.

Symbolically R-1 = {(b, a): (a, b) ∈ R for all a ∈ A and b ∈ B}.

A relation R on a set A is said to be identity relation on A if R = {(a, b): a ∈ A, b ∈ A and a = b}.

A relation R from A to B is said to be the universal relation, if R = A × B.

A relation R from A to B is called an empty relation or a void relation from A to B if R = ø.

Calculation:

A = {3, 4, 5}

Cartesian product \(A× A\) = {(3, 3), (3, 4), (3, 5), (4, 3), (4, 4),(4, 5), (5, 3), (5, 4), (5, 5)}

Given, R = {(a, b): a, b ∈ A, a divides b and b divides a}

R^-1 = {(b, a): a, b ∈ A, b divides a and a divides b}

If b divides a and a divides b. it is only possible if a = b.

Hence, relation R^-1 = {(3, 3), (4, 4), (5, 5)}. therefore R^-1 is an identity relation.