Proof by cases

Builds on Mathematical proof Disjunction Implication

Summary

A proof by cases splits the situation into a finite number of cases that cover all possibilities. Then it proves the statement in each case. The basic form is this rule: from $p \lor q$ , $p \to r$ and $q \to r$ , conclude $r$ .

Remarks

Another name is proof by exhaustion, mainly when the cases are many. Example: $n^2 + n$ is even for each integer $n$ . If $n$ is even, $n^2$ and $n$ are even. If $n$ is odd, $n^2$ and $n$ are odd. In both cases, the sum is even. A split into $p$ and $\neg p$ uses the law of excluded middle.

Reading path

To understand this page from the ground up, read these 6 pages in order. The foundations come first.

Show the path as a graph

Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.

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Proposition concept
Disjunction definition
Implication definition
Modus ponens concept
Mathematical proof concept
Proof by cases concept

Tag	`0WCP0PVET6`
URI	`m2://0WCP0PVET6`
Aliases	`proof-by-exhaustion`, `case-analysis`
Kind	concept
Writing	W0 stub
MSC	00A35
Specializes	Mathematical proof
Part of	Proof methods
Uses	Mathematical proof, Disjunction, Implication
Same as	Wikidata Q9299950 Wikipedia Proof by exhaustion

Proof by cases

Summary

Remarks

Reading path

Further reading

What this page needs for W1

What links here

Proofs that use this method