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Venn diagram problem

paulmdrdo

Active member
May 13, 2013
386
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.
Venn1.3.jpg
 

Plato

Well-known member
MHB Math Helper
Jan 27, 2012
196
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 $A\cap C\ne \emptyset$

Untitled.gif
 

Mathelogician

Member
Aug 6, 2012
35
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
Feb 2, 2012
409
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:

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