To echo the comments before this one: a) lots of people do have an intuition for Venn diagrams. Just look at the number of Venn diagram gags on xkcd. b) it is

To echo the comments before this one: a) lots of people do have an intuition for Venn diagrams. Just look at the number of Venn diagram gags on xkcd. b) it is a great mental image to have if you move on to measure theoretic probability.