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