Here's a random math/logic-book exercise I'd like to see:
The picture above shows a door with triple locks. Answer the following questions:
(a) Do you need the key to the top lock to enter this door? Yes.
(b) Will you be able to enter this door if you have only the key to the top lock? No.
(c) What's the technical term for this relationship? Necessary but not sufficient.
[Photo by LiGhtSynC under CC2.]