# Set Theory Proof

cmajor47

## Homework Statement

For all sets A and B, if A $$\subseteq$$ B then Bc $$\subseteq$$ Ac.

## 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!