Proof by Cases

  Proof by cases is used several ways and involves the connective or. We will be trying to prove a sentence of the type . This type of proof utilizes the tautology

The proof is accomplished by proving the antecedent of this sentence,

Hence, and must be proved. Any mode of proof for conditional sentences can be used.

Similarly, a proof by cases of

is accomplished by proving .

The art of producing a proof by cases lies in the discovery of what set of exhaustive cases is appropriate.