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With P being the power set,

P(~A) = P(U) - P(A) and

P(A-B) = P(A) - P(B)

I'm told if it's true to prove it, and if false to give a counterexample.

To be they're both false, since the null set is part of any power set, the subtraction of two power sets would get rid of the null set and the result could never be another power set. Am I wrong in assuming this?

Thanks in advance.