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

Define the relation AR 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.

Define the relation AR 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.