# Mark the correct alternative in the following question:

Question:

Mark the correct alternative in the following question:

Consider a 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

Solution:

We have,

$R=\{(a, b): a$ is brother of $b\}$

Let $(a, b) \in R$. Then,

$a$ is brother of $b$

but $b$ is not necessary brother of $a$                  (As, $b$ can be sister of $a$ )

$\Rightarrow(b, a) \notin R$

So, $R$ is not symmetric

Also,

Let $(a, b) \in R$ and $(b, c) \in R$

$\Rightarrow a$ is brother of $b$ and $b$ is brother of $c$

$\Rightarrow a$ is brother of $c$

$\Rightarrow(a, c) \in R$

So, $R$ is transitive

Hence, the correct alternative is option (b).