This is an interactive website to help you learn how to write a set theory proof. You should try to prove the statement yourself, and use the information on this webpage to check your work or to get a hint if you need one.

We will prove one part of DeMorgan's Laws. You will prove the other in your homework.
**You can see that most of the proof is missing.**
Click on the boxes to reveal the missing expressions.

But * before you click*, try to write the proof yourself and figure out what will appear!

If you wish to make the text disappear again, refresh the page.

*Prove that \((A\cup B)^c=A^c \cap B^c\).*

*Proof:* Let .
Then ,
so . From this
we learn that .
Therefore, .

Conversely, let

. Then , so . Thus , which implies that .We have proven that \((A\cup B)^c\subseteq A^c \cap B^c\) and \(A^c \cap B^c\subseteq(A\cup B)^c\), therefore \((A\cup B)^c=A^c \cap B^c\).