# Venn diagram problem

#### paulmdrdo

##### Active member
Find a Venn diagram containing three sets A, B, C such that $A\cap B\,\neq\,\emptyset$, $B\cap C\,\neq\,\emptyset$,and $C\cap A\,\neq\,\emptyset$, but $A\cap B\cap C\,=\,\emptyset$.

#### Plato

##### Well-known member
MHB Math Helper
Find a Venn diagram containing three sets A, B, C such that $A\cap B\,\neq\,\emptyset$, $B\cap C\,\neq\,\emptyset$,and $C\cap A\,\neq\,\emptyset$, but $A\cap B\cap C\,=\,\emptyset$.

View attachment 1127
What you have is not $A\cap C\ne \emptyset$

#### Mathelogician

##### Member
You don't have to use perfect circles in Venn diagrams. Try more complex figures!
Also you don't have to show the intersections with shadows only! You can try figures containing objects.

#### soroban

##### Well-known member
Hello, paulmdrdo!

Find a Venn diagram containing three sets $$A, B, C$$ such that:
$$A\cap B\,\neq\,\emptyset,\;B\cap C\,\neq\, \emptyset,\,\text{and }C\cap A\,\neq\,\emptyset$$
but $$A\cap B\cap C\,=\,\emptyset$$

View attachment 1127
No.
You have: $$C \cap A \,=\,\emptyset$$

The diagram might look like this:

Code:
              *               *
*   *           *   *
*       *       *       *
*           *   *           *
*       A       *       B       *
*               *:::*               *
*               *:::::::*               *
*               *:::*               *
*               *               *
*     *-----*---*-----*     *
*   |:::*       *:::|   *
* |:*           *:| *
*               *
|       C       |
|               |
|               |
|               |
*---------------*