Proving the Complementation Law for sets I am new to Discrete Mathematics, and have been asked to prove the Complementation Law for sets, that is: $\overline {(\overline A)} \equiv A$. Our teacher advised us to turn the sets into propositions, so would it be as simple as this: $\overline {(\overline A)}$ $\equiv \neg (\neg p)$ $\equiv p$ $\equiv A$ We have not really seen what a real proof looks like. Thank you!

For arbitrary $x$ we have:

If $x\in A$ then $x\
otin \overline{A}$ so $x\in\overline{\overline{A}}$. So $A\subseteq \overline{\overline{A}}$

And vice versa: If $x\in \overline{\overline{A}}$ then $x\
otin {\overline{A}}$ so $x\in A$ and now we have $\overline{\overline{A}}\subseteq A$

So $A=\overline{\overline{A}}$