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Consider the non-empty set consisting o...

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

Text Solution

Verified by Experts

The correct Answer is:
B
Given, aRb `implies `a is brother of b
` :.` aRa `implies` a is brother fo a, which is not true.
So, R is not reflexive.
aRb `implies` a is brother of b.
This does not mean b is also a brother of a and b can be a sister fo a.
Hence, R is not symmetric.
aRb `implies` a is brother of b
and bRc `implies ` b is a brother of c.
So, a is brother fo c.
Hence, R is transitive.
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