Proof of Set Theory: A \subseteq B implies Bc \subseteq Ac

[cmajor47]

Homework Statement

For all sets A and B, if A \subseteq B then B^c \subseteq A^c.

Homework Equations

The Attempt at a Solution

Proof: Suppose A and B are sets and A \subseteq B.
Let x \in B^c
By definition of complement, if x \in B^c then x \notin B
Since x \notin B, x \notin A
Since x \notin A, x \in A^c by definition of complement
Therefore if A \subseteq B then B^c \subseteq A^c.

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

 

[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.