Consider a non-empty set consisting of children in a family and a relation R defined as a R B if a is brother of b. Then, R is

Question

Philoid · Accepted Answer

R: a R b ⟺ a is a brother of b.

If a is a brother of b, then that does not necessarily mean b is a brother of a, since b can be a sister of a too. Hence, if (a, b) ∈ R, then (b, a)∉R always. Hence R is not symmetric.

If a is a brother of b and b is a brother of c, then a has to be a brother of c. Hence if (a, b) and (b, c) belongs to R, then (a, c) will belong to R. Hence, R is transitive.