# Set Theory Proof

1. Apr 4, 2009

### cmajor47

1. The problem statement, all variables and given/known data
For all sets A and B, if A $$\subseteq$$ B then Bc $$\subseteq$$ Ac.

2. Relevant equations

3. The attempt at a solution
Proof: Suppose A and B are sets and A $$\subseteq$$ B.
Let x $$\in$$ Bc
By definition of complement, if x $$\in$$ Bc then x $$\notin$$ B
Since x $$\notin$$ B, x $$\notin$$ A
Since x $$\notin$$ A, x $$\in$$ Ac by definition of complement
Therefore if A $$\subseteq$$ B then Bc $$\subseteq$$ Ac.

I just want to make sure that this proof is correct and that there are no mistakes. Thanks!

2. Apr 4, 2009

### Dick

It's fine. You might want to enhance it's proofiness by stating the reason why x not in B implies x not in A as you gave a reason for the other lines.