Question

Assertion (A): A relation R on the set {1, 2, 3} defined as R = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3)} is an equivalence relation.

Reason (R): A relation that is reflexive, symmetric and transitive is an equivalence relation.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (А).

• Both Assertion (A) and Reason (R) are a true, but Reason (R) is not the correct explanation of the Assertion (A).

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (А).

Explanation:

The assertion is true because the relation R on set {1, 2, 3} is reflexive (1, 1; 2, 2; 3, 3), symmetric (1,2 and 2, 1) and transitive (pairs like (2, 1) and (1, 2) lead back to (2, 2)). The Reason is also true as it correctly defines an equivalence relation, and it provides the exact justification for why the assertion is correct.