Given that, relation R is defined as aRb if a is brother of b

Now,

aRa ⇒ a is brother of a, which is not true.

⇒ (a,a) ∉ R

⇒ R is not reflexive

aRb ⇒ a is brother of b but this does not mean that b is brother of a,b can be sister of a.

Thus, (a,b) ∈ R ⇒ (b,a) ∉ R

⇒ R is not symmetric.

aRb ⇒ a is brother of b and bRc ⇒ b is brother of c

⇒ a is a brother of c.

⇒ R is transitive.

Hence, R is transitive but not symmetric.