More complicated question on Venn diagrams involve the use of simultaneous equations, or the introduction of a dummy variable x.
Example
Sketch the Venn diagram.
(1)
(2)
Divide (1) by (2) to get
Substitute these into the equation
Then
and from (1)
We can draw the Venn diagram.
Example:
and
are independent.
and
Find the possible values of
and draw a possible Venn diagram.
Label the intersectionthen
and
Sinceandare independent
or
A possible diagram is shown below.
