1. Use element argument method to prove that for any two sets A and B, if A B, then P(A) P(B), where P(A) and P(B) are power sets of A and B respectively. You must state your reasons clearly for every statement in your proof.

(14 marks)

Proof.

Let A and B be sets, such that A B.

Let X P(A).

From definition of power set, X A.

Let y X.

.........................

........., y B.

Thus, from definition of subset, we have X B.

Hence, from the definition of power set, X P(B).

Therefore, from the definition of subset, we have P(A) P(B).

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