Proof by Cases

Here we introduce "proof by cases", which involves splitting a proposition into multiple cases, and then proving each one of the cases using (possibly) different logic. The example we do here is simple, but the idea is what is important (and how to solve the problem set as well).

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[robharwood]

A very nice addition to the topic of this video (and the next!) would be the proof technique of Conditional Proof, where one first temporarily assumes P, and from P derives Q, and then concludes that (P -> Q), and then dropping the temporary assumption of P but keeping the conclusion that P->Q.
Both Proof by Cases and Proof by Contradiction are specializations of this more general technique of Conditional Proof (also called Implication Introduction, among other names).