# Homework Help: Set theory proof homework

1. Jul 7, 2009

### pinkyjoshi65

1. The problem statement, all variables and given/known data

1)Prove for all sets A and B contained in a universe U, if A intersection B' = nullspace then
P(A) − P(B) is a subset of P(A − B).

2)Prove for all sets A and B contained in a universe U, if A intersection B = nullspace then
P(A) − P(B) is a subset of P(A − B).

3)Prove for all sets A and B contained in a universe U, if A intersection B' = nullspace and
A intersection B = nullspace, then P(A) − P(B) is not a subset of P(A − B).

2. Relevant equations

I've trired some. I just need to know if the first one is correct. I don't know how to do the other 2. Please help me asap. Thanks.

3. The attempt at a solution

1) A inter B = nullspace...Hence A inter B is a subset of nullspace and nullspace is a subset of A inter B.
Hence nullspace is a subset of A and is a subset of B'-----(a)
Hence nullspace belongs to P(A) and also to P(B')
Hence nullspace belongs to P(A)-P(B).
From (a) we have nullspace is a subset of A and is not a subset of B
Hence nullspace is a subset of (A-B)
Hence nullspace belongs to P(A-B)
therefore P(A)-P(B) is a subset of P(A-B)

2. Jul 8, 2009

### g_edgar

This is invalid: Hence nullspace belongs to P(A)-P(B).

Things you stated up to that point are true, but mostly not of much use, since the nullset is automatically a subset of any set (in particular of A and B and B' and...)

3. Jul 8, 2009

### pinkyjoshi65

So what do you suggest i do?

4. Jul 8, 2009

### g_edgar

Review the definitions of the items in the statement of the problem.

5. Jul 8, 2009

### pinkyjoshi65

let x belong to P(A)-P(B)
so x is a subset of A and is not a subset of B
so x is a subset of (A-B)
so x belongs to P(A-B)
hence P(A)-P(B) is a subset of P(A-B)

6. Jul 8, 2009