question_answer 64)

Given a non empty set X, consider P(X) which is the set of all subsets of X. Define the relation R in P(X) as follows :       For subsets A, B in P(X), ARB if and only if . Is R an equivalence relation on P(X). Justify your answer.  

Answer:

We know that a set is subset of itself 3              is reflexive.       Also, let A, B  therefore ARB       But  need not imply .        does not imply BRA. So, R is not an equivalence relation.