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## Homework Statement

For all sets A and B, if A [tex]\subseteq[/tex] B then B

^{c}[tex]\subseteq[/tex] A

^{c}.

## Homework Equations

## The Attempt at a Solution

Proof: Suppose A and B are sets and A [tex]\subseteq[/tex] B.

Let x [tex]\in[/tex] B

^{c}

By definition of complement, if x [tex]\in[/tex] B

^{c}then x [tex]\notin[/tex] B

Since x [tex]\notin[/tex] B, x [tex]\notin[/tex] A

Since x [tex]\notin[/tex] A, x [tex]\in[/tex] A

^{c}by definition of complement

Therefore if A [tex]\subseteq[/tex] B then B

^{c}[tex]\subseteq[/tex] A

^{c}.

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