# Sets

• Nov 2nd 2008, 06:41 AM
captainjapan
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.
• Nov 2nd 2008, 07:52 AM
Plato
It is true that if $X\in P(A)\cup P(B)$ then X is a subset of A or a subset of B in either case X is a subset of $A \cup B$.
That is the only direction it is valid.
• Nov 3rd 2008, 01:34 PM
captainjapan
How would i provide a counterexample for this problem.

Thanks
• Nov 3rd 2008, 01:39 PM
Plato
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.
• Nov 3rd 2008, 11:18 PM
MRFLUFFY
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