Suppose that, A and B are sets such that the power set of A is a subset of the power set of B. Does it follow that, A is a subset of B?

Step 1</p>

It is given that

We need to show that

A power set of any set S is the set of all subsets of S,including the empty set and the set S itself.

Step 2</p>

Therefore let

Since

Therefore for we got .