# Q.8 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.

Given a non empty set X, consider P(X) which is the set of all subsets of X.

Since, every set is subset of itself , ARA  for all

R is reflexive.

Let

This is not same as

If        and

then we cannot say that B is related to A.

R is not symmetric.

If

this implies

R is transitive.

Thus, R is not an equivalence relation because it is not symmetric.

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