
Sets
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.

It is true that if $\displaystyle X\in P(A)\cup P(B)$ then X is a subset of A or a subset of B in either case X is a subset of $\displaystyle A \cup B$.
That is the only direction it is valid.

How would i provide a counterexample for this problem.
Thanks

It see to me that you simply post a question and expect someone to answer it.
I do not recall seeing any work that you have attempted.
So why don’t you start on this one?
Do something for yourself.

I AGREE
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