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 ______.

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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. Explanation: 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.

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