Question

Consider the non-empty set consisting of children in a family and a relation $R$ defined as $aRb$ if $a$ is brother of $b$. Then $R$ is

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

Answer 1

Answer: (B)

Given $aRb \Rightarrow a$ is brother of $b$.
But $b\, \not \,R \,a \,[ \because b$ may or may not be brother of $a]$
$\therefore R$ is not symmetric.
Let $aRb$ and $bRc$
$ \Rightarrow a$ is brother of $b$ and $b$ is brother of $c$.
$\therefore a$ is brother of $c \Rightarrow (a$, $c)\in R$.
$\therefore R$ is transitive.