Let A be a non-empty set. Statement 1: Identity relation on A is Reflexive. Statement 2: Every…

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.

(a)Both the statements are true.
(b)Both the statements are false.
(c)Statement 1 is true and Statement 2 is false.
(d)Statement 1 is false and Statement 2 is true.

Answer

Correct option: (c)

Answer: (c) Statement 1 is true and Statement 2 is false. The identity relation $\{(a,a)\}$ is reflexive, so Statement 1 is true. The universal relation $A \times A$ is reflexive but is not the identity relation when $A$ has more than one element, so Statement 2 is false.