Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b, Then R is

Transitive but not symmetric

Given that a R b ⇒ a is brother of b.

This does not mean b is also brother of a as be can be a sister of a

Therefore, R is not symmetric

a R b ⇒ a is brother of b ⇒ & b R c ⇒ b is brother of c.

So, a is brother of c.

Thus, R is transitive.

So option 2 is correct, transitive but not symmetric.