It is true that if then X is a subset of A or a subset of B in either case X is a subset of .
That is the only direction it is valid.
a. Prove that if A and B are sets, then P(A) ∪ P(B) ⊆ P(A ∪ B).
b. Give a counterexample for the following statement: if A and B are sets, then P(A) ∪ P(B) = P(A ∪ B).
c. Fill in the blank in the simplest way possible that makes the following statement true: P(A) ∪ P(B) = P(A ∪ B) if and only if . Prove that your answer is correct; of course, you may use your solution to part (a) as a lemma.
I agree with Plato on this L.G., you need to stop posting your math assignments and expecting people to do them for you, if you keep this up you will surely fail that test you have on Nov 12