# Consider a non-empty set consisting of children in a family and a relation R defined as a R B if a is brother of b. Then, R isA. symmetric but not transitiveB. transitive but not symmetricC. Neither symmetric nor transitiveD. both symmetric and transitive

R: a R b a is a brother of b.

If a is a brother of b, then that does not necessarily mean b is a brother of a, since b can be a sister of a too. Hence, if (a, b) R, then (b, a)R always. Hence R is not symmetric.

If a is a brother of b and b is a brother of c, then a has to be a brother of c. Hence if (a, b) and (b, c) belongs to R, then (a, c) will belong to R. Hence, R is transitive.

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