MA 175 Discrete Math Proof Schemas

Direct Proof (conditionalization)

Introduction of the universal quantifier

Direct Proof (generalization)

Elimination of the universal quantifier

Existential quantifier introduction

Bi-Existential Inference

Proof by cases

Proof by contraposition

Proof by contradiction

Mathematical Induction (language of properties)

Mathematical Induction (language of sets)

Prove by contradiction

assume P and ¬Q and derive a contradiction

assume both P and ¬Q, and deduce some other contradiction R∧¬R.

Prove the contrapositive

assume ¬Q and show ¬P

prove P→Q by assuming ¬Q and reasoning until you obtain ¬P.