p ⊃ q
p
∴ q
Modus Ponens
p ⊃ q
~ q
∴ ~p
Modus Tollens
Modus Tollens
p ⊃ q
~ q
∴ ~p
Modus Ponens
p ⊃ q
p
∴ q
p ⊃ q
q ⊃ r
∴ p ⊃ r
Hypothetical syllogism
Hypothetical Syllogism
p ⊃ q
q ⊃ r
∴ p ⊃ r
p V q
~ p
∴ q
disjunctive syllogism
disjunctive syllogism
p V q
~ p
∴ q
(p ⊃ q) * (r ⊃ s)
p V r
∴ q V s
Constructive Dilemma
Constructive Dilemma
(p ⊃ q) * (r ⊃ s)
p V r
∴ q V s
p ⊃ q
∴ p ⊃ (p * q)
Absorption
Absorption
p ⊃ q
∴ p ⊃ (p * q)
p * q
∴ p
Simplification
Simplification
p * q
∴ p
p
q
∴ p * q
Conjunction
Conjunction
p
q
∴ p * q
p
∴ p V q
Addition
Addition
p
∴ p V q