Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

enter image description here

share|improve this question
2  
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

3 Answers 3

up vote 8 down vote accepted

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.

share|improve this answer
    
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.

share|improve this answer
    
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.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.