Lecture3

Theorems and Proofs

Axiom /Postulate(公理，基本原理), Theorem, Lemma(引理), premises(前提)

Rules of Inference

否定后段式

-|q

p --> q
----------
 -| p

三段式

p --> q
q --> r
-------
So p --> r

Inference for Quantified Statement

\-/ x

Ex
Existential Generalization(EG)

P(c) for some element c
------------------------
E x

Methods to proof

Direct proof: p --
Contradiction: p^
Case: (分类讨论)
Equivalence
Vacuous Proof: p-->q. If q is false, p-->q is t
Trival : p-->q. If is q is true, p-->q is f

Asignmetn