Logic Rules

Rules of Replacement

100

~ (p * q) = (~p v ~q)

De Morgans

200

[p * (q v r)] = [(p * q) v (p * r)]

distribution

300

(if p then q) = (~p v q)

material implication

Rules of Inference

100

if p then q

p 

therefore q

modus ponens

200

p v q

~p

therefore q

disjunctive syllogism

300

if p then q

if q then r

therefore, if p then r

hypothetical syllogism

400

p * q

therefore, p

simplification

500

p

therefore, p v q

addition

Rules of Replacement

100

(p v q) = (q v p)

Commutation

200

p = ~~p

double negation

300

[(p*q) then r] = [if p then (if q then r)]

exportation

400

(p=q) = [(if p then q) * (if q then p)]

material equivalence

500

(p=q) = [(p * q) v (~p * ~q)]

material equivalence

Rules of Inference

100

if p then q

~q

therefore ~p

modus tollens

200

p 

q

therefore p * q

conjunction

300

(if p then q) * (if r then s)

p v r

therefore, q v s

constructive dilemma

400

if p then q

therefore, if p then (p * q)

absorption

Rules of Replacement

100

[p v (q v r)] = [(p v q) v r]

association

200

(if p then q) = (if ~p then ~q)

transposition

300

p = (p v p)

p = (p * p)

tautology