Set theory problem

**jmedsy** · September 4th 2011, 02:51 PM

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

**Plato** · September 4th 2011, 04:28 PM

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?

**ModusPonens** · September 4th 2011, 05:16 PM

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).

**Plato** · September 4th 2011, 05:20 PM

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.

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