One counter-example ends a claim

A claim passes a hundred tries. Is that enough to trust it?

The rule

No: a case nobody tried can still break the claim.

A counter-example is one case where a claim fails. A claim that says always is false if one case fails.

Take the claim "two sides and an angle always make one triangle." Take sides 8 and 5, with 30° next to the 8. Those measurements build two triangles. That one case ends the claim.

The other direction matters too. A search that finds no failure is not a proof. It only shows the claim held in the cases someone tried. A proof covers every case.

Try cases on each claim. Does any case break it?

Try the lab to finish this lesson.