Show your work 1 Prove If A g B then P A C PB SolutionIt is

Show your work. 1. Prove: If A g B, then P (A) C P(B).

Solution

It is given that A and B are sets and AB. Now, suppose that S is any element of P(A). Thus by the definition of power set, S must be a subset of A.

Since SA and AB, therefore SB.

Now, since SB, the difinition of power set implies that S P(B).

Since we have shown that any element of P(A) is also an element of P(B), we get P(A) P(B).