Venn diagram problem

[paulmdrdo]

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 $A\cap B\cap C\,=\,\emptyset$.

here's my answer please check if it is right.

 

[Plato]

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 $A\cap B\cap C\,=\,\emptyset$.

here's my answer please check if it is right.
View attachment 1127

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

 

[Mathelogician]

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]

Hello, paulmdrdo!

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

Here's my answer; please check if it is right.
View attachment 1127
No.

You have: [tex]C \cap A \,=\,\emptyset[/tex]


The diagram might look like this:

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