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?
Venn diagram for $(\sim A) \cap (\sim B) \cap (\sim C)$
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elementary-set-theory
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2Your 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. – 2012-07-11
3 Answers
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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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0@LF4 Yes. Your diagram is indeed right, where $U$ denotes the gray shaded area in the above picture. – 2012-07-11
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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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0Thanks, 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. – 2012-07-11
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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.