Choose the correct answer from the given four options.Consider th… - Vidyadip

MCQ

Choose the correct answer from the given four options.Consider the non-empty set consisting of children in a family and a relation $R$ defined as $\text{aRb}$ if a is brother of $b.$ Then $R$ is:

A
Symmetric but not transitive.
✓
Transitive but not symmetric.
C
Neither symmetric nor transitive.
D
Both symmetric and transitive.

✓

Answer

Correct option: B.

Transitive but not symmetric.

We are given that a relation $R$ defined $\text{aRb} \Rightarrow a$ is brother of $b.$
$aRa \Rightarrow a$ is brother of $a,$ which is not true.
Hence$, R$ is not reflexive.
$aRb \Rightarrow a$ is brother of $b.$
This does not mean $b$ is also a brother of $a$ and $b$ can be a sister of $a.$
Hence, it is not symmetric.
$aRb \Rightarrow a$ is brother of $b$
and $bRc \Rightarrow b$ is a brother of $c.$
So$, a$ is brother of $c.$
Hence$, R$ is transitive.

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