Question:
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
(A) symmetric but not transitive
(B) transitive but not symmetric
(C) neither symmetric nor transitive
(D) both symmetric and transitive
Solution:
(B) transitive but not symmetric
aRb ⇒ a is brother of b.
This does not mean b is also a brother of a as b can be a sister of a.
Thus, R is not symmetric.
aRb ⇒ a is brother of b.
and bRc ⇒ b is brother of c.
So, a is brother of c.
Therefore, R is transitive.