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5. Recall that P(A) denotes the power set of A, that is, the set of all

subsets of A.

(a) If A = {1,2,3} write down the set P(A). What is P(A)|?

(b) If B = {0, {1}, {2), (3), (1,2)) the notation B means the union

of all of the elements of B, so it is the set Øu{1}{2}U{3}U{1,2}.

What set is this written as simply as possible?

(c) For any sets A and B, prove that A = B if and only if P(A) =

P(B). (Remember "if and only if" is so you have to prove

and separately.)

Fig: 1