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 [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       |
              |               |
              |               |
              |               |
              *---------------*

 

[blue_raver22]

Your response is correct. The Venn diagram would have three overlapping circles representing sets A, B, and C, with each pair of circles intersecting, but the intersection of all three circles would be empty. This type of diagram is commonly used to represent sets with non-empty intersections between some pairs of sets, but no elements in common among all three sets. It can be useful in illustrating concepts such as mutual exclusivity or overlapping categories.