# 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 A ⊂ B. Is R an equivalence relation on P(X)? Justify your answer.

We know that every set is a subset of itself, ARA for all A ϵ P(X).

R is reflexive.

This cannot be implied to B A.

So, if A = {1, 2} and B = {1, 2, 3}, then it cannot be implied that B is related to A.

R is not symmetric.

So, if ARB and BRC, then A B and B C.

A C

R is transitive.

Therefore, R is not an equivalence relation since it is not symmetric.

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