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(D) Let $R$ be the relation defined by $xRy$ if $x$ is a brother of $y$. $1$. Reflexive: $A$ person cannot be a brother of themselves. Thus,$xRx$ is f

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None of these

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(D) Let $R$ be the relation defined by $xRy$ if $x$ is a brother of $y$. $1$. Reflexive: $A$ person cannot be a brother of themselves. Thus,$xRx$ is false. So,it is not reflexive. $2$. Symmetric: If $x$ is a brother of $y$,then $y$ is a brother of $x$ (assuming $y$ is male). However,if $y$ is a sister,$y$ is not a brother of $x$. In the context of the relation '$x$ is a brother of $y$',if $x$ is a brother of $y$,it does not necessarily imply $y$ is a brother of $x$ (e.g.,if $y$ is a girl). $3$. Transitive: If $x$ is a brother of $y$ and $y$ is a brother of $z$,then $x$ is a brother of $z$. This holds true. Given the standard interpretation of this problem in textbooks,the relation '$x$ is a brother of $y$' is typically considered neither reflexive,nor symmetric,nor transitive in a general sense. However,if we assume the set consists only of brothers,it would be symmetric and transitive. Given the options,the most appropriate answer is that it is not reflexive,symmetric,or transitive. Therefore,the correct choice is $(d)$.

Let $A$ be the non-void set of the children in a family. The relation '$x$ is a brother of $y$' on $A$ is

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