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Q. If $R=\{(x, y): x$ is father of $y\}$, then $R$ is

Relations and Functions - Part 2

Solution:

Here, $R$ is not reflexive; as $x$ cannot be father of $x$, for any $x , R$ is not symmetric as if $x$ is father of $y$, then $y$ cannot be father of $x$. $R$ is not transitive as if $x$ is father of $y$ and $y$ is father of $z$, then $x$ is grandfather (not father) of $z$.