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L
O
G
I
C
100

p ) q

p

* q

Modus Ponens

100

~(p . q) becomes

~ p v ~q

De Morgan's Theorems

100

p . q

* p

Simplification

100

From (p) derive

p v q

Addition

100

p ) q 

q 

* p

Affirming the Consequent

200

p ) q

q ) r

* p ) r

Hypothetical Syllogism

200

~~ p becomes p

Double Negation

200

p . q

becomes

q . p

Commutation

200

p v q

~ p

* q 

Disjunctive Syllogism

200

p ) q 

~ p 

* ~  q

Denying the Antecedent

300

p 

q 

* p . q

Conjunction

300

p ) q 

~ q

* ~ p

Modus Tollens

300

(p ) q) becomes

(~p v q)

Material Implication

300

(p . q) . r 

becomes

p . (q . r)

Association

300

p v q

p

*q

Affirming a Disjunct

400

(p = q) =

[(p ) q) .            

( q ) p)]


Material Equivalence

400

(p ) q) . (r ) s)

p v r

* q v s

Constructive Dilemma

400

~ (p v q) becomes

(~ p . ~q)

De Morgan's Theorems

400

p ) q becomes 

~ q ) ~p

Transposition

400

p v q 

q

* q

Affirming a Disjunct

500

(p ) r) . (q ) s)

p v q

* r v s

Constructive Dilemma

500

p v (q . r)

becomes

(p v q) . (q v r)

Distribution

500

p . (q ) r)

* p

Simplification

500

p . p becomes 

p

Tautology

500

p ) q 

q ) r 

r

* p

Affirming the Consequent