I point you towards a website I've been contributing to for some few weeks now ... here's the page containing some proofs that might help.
Subset Equivalences - Proofwiki.org
explore and enjoy.
I have 2 problems that are annoying the heck out of me...
#1. If A is contained in B prove that (C\B) is contained in (C\A) Either prove the converse is true or give a counterexample. Don't even know where to start. It is only the first week of the course, so I just need pretty basic help.
#2. Under what conditions does A\(A\B)=B. Again, how do I start this?
I point you towards a website I've been contributing to for some few weeks now ... here's the page containing some proofs that might help.
Subset Equivalences - Proofwiki.org
explore and enjoy.
Is B a null set?
Because say A={1, 2, 3, 4, 5} and B={1, 2,3}.
We get:
A\({4,5}
={1,2, 3}
If B is a null set, and A is the same, we get:
A\{1, 2, 3, 4, 5}.
={}
Therefore, we have B.
Also, what about A=B? A = {1, 2 , 3, 4, 5} and B={1,2, 3, 4, 5}
A\({}
{1,2,3,4,5}
Therefore, we get B.
So, these 2 cases appear to work. these are my thoughts so far.
I just looked at #1.
Clearly, we have the following identities
- if , then , where stands for the compliment of the sets.
- if , then
Hence, from the properties above, we get implies . Intersection both sides with , we get , which is equivalent to .
I hope you may easily find #2 by using 3. for twice and thinking on the resultant situation.
Note. The easiest way to work on such problems may be using Venn diagrams.