Logic 101 (#46): Proof By Cases (Killer Proof Strategy #3)

This lecture introduces the proof strategy known as proof by cases. It exploits a setup with two implications featuring the same consequent and a disjunction featuring the antecedents of those implications. With that information, it is easy to conclude that the consequent is true.

In practice, the hard part of proof by cases is usually setting up the implications. This lecture gives an example where using conditional proofs can solve that problem.

[ramonarielkengarcia]

Can we also use direct proof for this?
4 (R v P) v (S v Q) | 3 Disjunction Introduction
5 (R v S) v (P v Q) | 4 Associativity, Commutativity
6 T v T | 1, 2, 5 Constructive Dilemma
7 T | 6 Idempotence

[d_]

I would like to thank you for introducing logic in such an invaluable and easily digestible way! Will you ever do predicate logic videos? We desperately need them. Anyone who agrees please like my comment!

[PunmasterSTP]

Proof by cases? More like "you're holding aces", because I imagine these videos would beat any others trying to cover the same material. Thanks for making such high-quality educational content!

[lea]

First I apply constructive dilemma to the premises and get (R or R). Then I use the RR of idempotence and convert the concclusion into simply R and I think that is all in two steps.

[gidrengidrenovi]

RvR 1, 2, 3 Constructive Dilemma
R 4. Idempotence
. Idempotence. Idempotence.

[MM-vxty]

I thought for assumption for conditional proof you had to use the whole antecedent

[slasachips]

can you also say that if p or q has to be true then you have a modus ponens on at least one of the 2?