1. ## Set theory problem

This is seemingly easy, but I'm having trouble finding a starting point. Please advise.

Prove:

$(C \backslash B) \subset (C \backslash A) \to (A \subset B)$

note: Some of you may be used to using C - B instead of C \ B

2. ## Re: Set theory problem

Originally Posted by jmedsy
Prove:
$(C \backslash B) \subset (C \backslash A) \to (A \subset B)$
Let $A=\{1,2,3\},~B=\{2,3,4\}~\&~C=\{3,4,5,6\}$.
Now is it true?

3. ## Re: Set theory problem

I think it's meant to be that A and B are subsets of C. C\(C\A) is a subset of C\(C\B).

4. ## Re: Set theory problem

Originally Posted by ModusPonens
I think it's meant to be that A and B are subsets of C. C\(C\A) is a subset of C\(C\B).
But that is not what was posted.
We can only deal with the OP.