Inference Rules Flashcards
Simplication (Simp)
(P & Q) (P & Q)
_______ __________
P Q
Conjuction (Conj)
P
Q
__________
(P & Q)
Additon (Add)
P
_______
(P v Q)
Modus Ponens (MP)
(P -> Q)
P
____
Q
Modus Tollens
(P -> Q)
~Q
_________
~P
Hypothetical Syllogism
(P -> Q)
(Q -> R)
_________
(P -> R)
Disjuction Elimaination (DE)
(P v Q)
(P -> R)
(Q -> R)
_________
R
Disjuctive Syllogism (DS)
(P v Q) (P v Q)
~P ~Q
______ ___________
Q P
Bioconditional Elimination (BE)
(P <-> Q) (P <-> Q)
P Q
___________ __________
Q P
Material Implication (MI)
(P -> Q) (~P v Q)
________ ___________
(~P v Q) (P -> Q)
Equivlence (E)
((P -> Q) & (Q -> P))
__________________
(P <-> Q)
Contraposition (C)
(P -> Q) (~Q -> ~P)
____________ ______________
(~Q -> ~P) (P -> Q)
Double Negatation (DN)
P ~~P
_____ ____________
~~P P
Demorgans Theorem (DT)
~ (P & Q) (~P v ~Q) ~(P v Q) (~P &~Q)
__________ __________ __________ __________
(~P v ~Q) ~(P & Q) (~P & Q) ~(P v Q)
