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Proof Rules
18 Proof Rules
18
Philosophy
Undergraduate 2
04/17/2012
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Cards

Term
Modus Ponens
 Definition
(A-B), A , so B
Term
Modus Tollens
 Definition
(A-B), ~B, so ~A
Term
Hypothetical Syllogism
 Definition
(A-B), (B-C), so (A-C)
Term
Disjunctive Syllogism
 Definition
(A v B), ~A, so B (A v B), ~B, so A
Term
Constructive Dilemma
 Definition
(A v B), (A-C), (B-D), so (C v D)
Term
Simplification
 Definition
(A * B), so B
(A * B), so A
Term
Conjunction
 Definition
A, B, so (A * B)
Term
Addition
 Definition
A, so (A v B)
Term
Double Negation
 Definition
A :: ~~A
Term
Communication
 Definition
(A v B) :: (B v A)
(A * B) :: (B * A)
Term
Association
 Definition
[A v (b v C)] :: [(A v B) v C]
[A * (B * C)] :: [(A * B) * C]
Term
DeMorgan's Law
 Definition
~(A * B) :: (~A * ~B)
~(A v C) :: (~A v ~B)
Term
Contraposition
 Definition
(A-B) :: (~B-~A)
Term
Distribution
 Definition
[A * (B v C)] :: [(A * B) v (A * C)]
[A v (B * C)] :: [(A v B) * (A * C)]
Term
Exportation
 Definition
[(A * B)-C] :: [A-(B-C)]
Term
Redundancy
 Definition
A :: A * A
A :: A v A
Term
Material Equivalence
 Definition
A IFF B :: [(A-B) * (B-A)]
A IFF B :: [(A * B) v (~A * ~B)]
Term
Material Implication
 Definition
(A-B) :: (~A v B)
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