Proof by exhaustion

Proof by exhaustion (also called proof by cases) is a way to prove that something is true. It starts by splitting a problem into different parts or cases. You then take each case one at a time and figure out if it is true or false, like a detective solving a mystery. If, at the end of all the cases, you have shown that everything is true, then you can be sure that the thing you are trying to prove overall must also be true. It's like doing a jigsaw puzzle—you try all the pieces until you fit them all together, and then you know you have the right answer.