Question

Let A be a non-empty set.

Statement 1: Identity relation on A is Reflexive.

Statement 2: Every Reflexive relation on A is an Identity relation.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true and Statement 2 is false.

• Statement 1 is false and Statement 2 is true.

Answer 1

Statement 1 is true and Statement 2 is false.

Explanation:

Consider A = {a, b, c} and define a relation R as R = {(a, a), (b, b), (c, c), (a, b).

Then R is a reflexive relation on A, but not an identity relation, because R contains the elements (a, b).