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Let the universal set be $U$ which is represented as the rectangular frame. Set $A$, $B$ and $C$ are the 3 circles on the left top, right top and the bottom, respectively.

The first diagram represents the $U$. The second diagram represent the complement of $A \cap B\cap C$. Etc... But what is the set operation corresponds to the last Venn diagram below?

enter image description here

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It's the empty set. As the empty set is unique the empty set notation would do, I guess. –  Kasun Fernando Aug 16 '12 at 15:36
@KasunFernando: If you are sure why didn't post it as your answer? –  stalking is prohibited Aug 16 '12 at 15:42
It's the intersection of the 2 diagrams preceding it. –  user2468 Aug 16 '12 at 18:34

3 Answers 3

up vote 3 down vote accepted

If the first one is the 'universe' $U$, the last is $U\setminus U = \emptyset$. The blank in the pictures means that we are subtracting something from the 'universe' $U$. As an example, the second figure, the blank is $A\cap B\cap C$, and therefore the orange remaining is $U\setminus (A\cap B\cap C)$.

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Kasun Fernando says in a comment, and I agree:


The empty set is denoted by $\emptyset$ (\emptyset in $\TeX$) or $\varnothing$ (\varnothing).

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That is called the Ballantine operation.

Ballantine Ale

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I tried to downvote this answer, but the software wouldn't let me. –  MJD Aug 16 '12 at 18:31
Stupid software doesn't let Mark downvote his own answer! –  GEdgar Aug 16 '12 at 18:50

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