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  4. Let A be the non-empty set of children in a family. The relation 'x is brother of y ' in A is:

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

Relations and Functions - Part 2

Solution:

Let $x_{1}, x_{2}, x_{3}$, are three brothers $x_{1} R x_{2}, x_{2} R x_{3}$
$\Rightarrow x _{1} Rx _{3}$ are element of relation ' $x$ is brother of $y$ '. So transitive.