Question

Consider the non-empty set consisting of children in a family. state giving reasons whether each of the following relations is (i) Symmetric (ii) Transitive
(a) x is a brother of y.
(b) x likes y.

Answer 1

(i) $\ne$ S, but T

(ii) $\ne S,\ne T$

(a) (i) The given relation is not symmetric, since if x is the brother of y, then y may be the sister of x. Thus in this case xRy but y(~R)x.

(ii) This relation is however transitive, since if x is the brother of y and y is the brother of z, then surely x is the brother of z.

(b) (i) Here the given relation is not symmetric since if x likes y then it is not necessary that y likes x.

(ii) This relation is not transitive since if x likes y and y likes z, then it is not necessary that x likes z.