Consider the non-empty set consisting of children

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.

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