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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 ______.
Options
Symmetric but not transitive
Transitive but not symmetric
Neither symmetric nor transitive
Both symmetric and transitive
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Solution
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 transitive but not symmetric.
Explanation:
aRb ⇒ a is brother of b.
This does not mean b is also a brother of a as b can be a sister of a.
Thus, R is not symmetric.
aRb ⇒ a is brother of b.
and bRc ⇒ b is brother of c.
So, a is brother of c.
Therefore, R is transitive.
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