MHB Find 3-Set Venn Diagram: A,B,C w/ Empty Intersection

[paulmdrdo1]

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

 

[Plato2]

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 $A\cap C\ne \emptyset$

View attachment 1128

 

[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 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

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

You have: C \cap A \,=\,\emptysetThe diagram might look like this:

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