Consider the non-empty set consisting of children in a family and a relation R defined by a R b 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 by a R b if a is brother of b then R is

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Both Symmetric and Transitive

Neither Symmetric nor Transitive

Transitive but not Symmetric

Symmetric but not Transitive

answer is B.

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Detailed Solution

‘a’ can not be a brother of ‘a’
$∴ (a, a) \notin R \forall a \in A$
R is not reflexive
$(a, b) \in R \Rightarrow' a'$ is brother of ‘b’ may not be a brother of a $∴ (b, a) \notin R$
R is not symmetric let
$\begin{array}{l} (a, b) \in R a n d (b, c) \in R \\ t h e n (a, c) \in R \\ ∴ R i s t r a n s i t i v e \end{array}$