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

Question

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 aRb if a is brother of b. Then R is:

Symmetric but not transitive.
Transitive but not symmetric.
Neither symmetric nor transitive.
Both symmetric and transitive.

✓

Answer

Transitive but not symmetric.

Solution:
We are given that a relation R defined aRb ⇒ a is brother of b.
aRa ⇒ a is brother of a, which is not true.
Hence, R is not reflexive.
aRb ⇒ 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 ⇒ a is brother of b
and bRc ⇒ b is a brother of c.
So, a is brother of c.
Hence, R is transitive.

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