1.2 Proof Methods | 1.2 Proof Methods | Unit 1: Proofs | Mathematics for Computer Science | Electrical Engineering and Computer Science

<Proof By Cases: Video
1.2.1Proof By Contradiction: Video
1.2.2Proof By Contradiction
1.2.3Proof By Cases: Video
1.2.4When to Prove by Cases
1.2.5Friends and Strangers
1.2.6A Bogus Proof by Cases
1.2.7A Bogus Proof by Contradiction
>Friends and Strangers

When to Prove by Cases

Based on the video and slides, when might we want to prove by cases?

The range of the variables in the problem can be broken up into pieces (i.e. cases).

The predicate in each case is easier to prove.

All cases together cover all possibilities, such that proving all individual cases completes the proof.

When a direct proof is infeasible.

Proof by cases might be used when a complicated proof could be broken into cases, where each case is simpler to prove and the cases together cover all possibilities.