# Venn diagram for $(\sim A) \cap (\sim B) \cap (\sim C)$

The way I read that it says everything that is not part of $A$,$B$ and $C$. So the answer is $U$ from my diagram?

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Your grey area avoiding $A$, $B$ and $C$ looks correct, but for some people this is not $U$ as $U$ can represent the universal set, i.e. everything in the rectangle. – Henry Jul 11 '12 at 2:35

Recall the De Morgan's law for sets. $$(\sim A) \cap (\sim B) \cap (\sim C) = \sim (A \cup B \cup C)$$ Now you should be able to conclude what you want.

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That's what I ended up doing but didn't know if my diagram was the correct way of displaying that information. – LF4 Jul 11 '12 at 2:34
@LF4 Yes. Your diagram is indeed right, where $U$ denotes the gray shaded area in the above picture. – user17762 Jul 11 '12 at 2:36

Yes! You can try shading each of $\sim\! A$, $\sim\! B$, and $\sim\! C$ in three different ways, and see where all three shadings occur.

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Thanks, I was a little confused how to create a Venn Diagram when none of the sets were used. It's the "Include everything besides what you have." That was throwing me for a loop. I didn't know if that was the correct way or not and all searching came up with no answers. – LF4 Jul 11 '12 at 2:33

Using D'Morgan's law, $\sim A\cap \sim B \cap\sim C=\sim(A\cup B\cup C)$ which is the region $U$. $\sim$ behaves like a negative sign and converts $\cap\to \cup$ and $\cup \to \cap$ and sets to their complements.

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