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)

transitive but not symmetric

Answer 2

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.