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 _____________ .

Question

KollegeApply · Accepted Answer

We have, R = {(a, b) : a is brother of b} Let (a, b) ∈ R. Then, a is brother of b but b is not necessary brother of a (As, b can be sister of a) ⇒ (b, a) ∉ R So, R is not symmetric Also, Let (a, b) ∈ R and (b, c) ∈ R ⇒ a is brother of b and b is brother of c ⇒ a is brother of c ⇒ (a, c) ∈ R So, R is transitive Hence, R is transitive but not symmetric.

AChoose Your Answer