Question

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

• A. reflexive but not symmetric
• B. symmetric and transitive
• C. neither reflexive nor symmetric nor transitive
• D. Symmetric but not reflexive

Answer 1

Answer: (C)

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 $z$.