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- StudyBlue
- Washington
- Western Washington University
- Philosophy
- Philosophy 102
- Daniel/howard-snyder
- Inference Rules for Statement Logic

Nick F.

Modus Ponens (MP)

p --> q

p

:. q

Modus Tollens (MT)

p --> q

~q

:. ~p

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Disjunctive Syllogism (DS)

p v q p v q

~p ~q

:. q :. p

Simplification (Simp)

p**.**q p**.**q

:. p :. q

Conjunction (Conj)

p

q

:. p**.**q

Hypothetical Syllogism (HS)

p --> q

q --> r

:. p --> r

Addition (Add)

p p

:. p v q :. q v p

Constructive Dilemma (CD)

p v q

p --> r

q --> s

:. r v s

Double Negation (DN)

p : : ~~p

Commutation (Com)

(p v q) : : (q v p)

(p**.**q) : : (q**.**p)

Association (As)

(p v (q v r)) : : ((p v q) v r))

(p**.**(q**.**r)) : : ((p**.**q)**.**r)

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De Morgan's Laws (DeM)

~(p**.**q) : : (~p v ~q)

~(p v q) : : (~p**.**~q)

Contraposition (Cont)

(p --> q) : : (~q --> ~p)

Exportation (Ex)

((p**.**q) --> r) : : (p --> (q --> r))

Distribution (Dist)

(p**.**(q v r)) : : ((p**.**q) v (p**.**r)

(p v (q**.**r)) : : ((p v q)**.**(p v r)

Redundancy (Re)

p : : (p**.**p)

p : : (p v p)

Material Equivalence (ME)

(p <-> q) : : ((p-->q)** .** (q-->p))

(p <-> q) : : ((p**.**q) v (~p **.** ~q))

Material Implication

(p-->q) : : (~p v q)

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