What does it mean that mutually exclusive and collectively exhaustive?

The best category systems have no overlaps and no gaps.

Example: You're triaging customer support tickets into Billing, Technical, and Account Management. A customer writes: 'I can't log in and I think I was charged twice.' That ticket belongs in two buckets simultaneously — which means your categories aren't mutually exclusive. And if a customer asks about your public API docs, none of those three buckets fit — which means your categories aren't collectively exhaustive. The fix isn't to force every ticket into one category. The fix is to redesign the categories until every ticket lands in exactly one.

Try this: Pick one category system you use daily — email folders, project labels, task statuses, note tags. Write down every category. Then ask two questions: (1) Can any single item legitimately belong in two or more of these categories? If yes, you have an overlap — your categories aren't mutually exclusive. (2) Can you think of any item that doesn't fit any category? If yes, you have a gap — your categories aren't collectively exhaustive. Redesign the categories to eliminate both problems. If you can't achieve both, decide which violation you'll tolerate and document why.