Hello!!! Please help meeeeeee!! I am just doing some homework problems for my test and I come across this one I don't understand.
1) Is it possible to find set A and B such that both A in B and A subset of B are true? Give an example or prove this is impossible.
[y in (A-C)-(B-C)] iff [y in (A-C) and y not in (B-C)] iff [(y in A and y not in C) and y not in (B-C)]
But [(y not in C) and (y not in (B-C))] iff [y not in B], so:
[y in (A-C)-(B-C)] iff [y in A and y not in C and y not in B]
The final steps are trivial, what we have shown is that [x in (A-B)-C] iff
[x in (A-C)-(B-C)]
Informally the process involved in a proof is just to expand what the two
expressions mean, and you evantualy find that they mean the same thing.