You can use OmniGraffle, the powerful tool for graphics, diagrams, and visuals in general, to create the popular Venn diagrams. All you need is to create an initial circle, then copy it and overlap both.

Next step is to copy and paste both overlapping diagrams, now you have a pair of diagrams.

Here comes the most important step, from the inspector menu (if you don’t see it, show it from the menu Inspectors/Show Inspectors), go to the Shape section. Now select the diagram on top and then click on the mid button “Intersect shapes“.

This will be the result, the intersection of the two circles has been cut.

Now you can color the intersection and overlap to the first diagram.

And playing with solid fills you can achieve the desired Venn diagram.

Venn diagrams using transparency

You can also rely on shapes’ transparency to achieve a similar effect, so create circles of the desired color, set the transparency of the fill color to something like 50%, and then overlap the circles.

Using the same color as before, the result will be: