Proving Set Theory Equations with Nullspace Intersection

[pinkyjoshi65]

Homework Statement

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).

Homework 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.

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)

 

[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...)

 

[pinkyjoshi65]

So what do you suggest i do?

 

[g_edgar]

So what do you suggest i do?

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

 

[pinkyjoshi65]

how about i do this:

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)

 

[pinkyjoshi65]

someone please help

 

[g_edgar]

how about i do this:

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

a good start

so x is a subset of (A-B)

does not follow