Rules of Inference
psupsetq
p
:.q
What is Modus Ponens?
psupsetq
~q
~p
What is Modus Tollens?
This theorem states that the following are equivalent:
~(p*q), (~pvv~q)
What is De Morgan's Theorem?
This rule of replacement states the following:
~ ~p-=p
What is the rule of Double Negation?
The rule of Double negation states that
~ ~p
decomposes as this
What is
p?
It decomposes as
p
~q
What is the Conditional or
~(psupsetq)?
p
:.pveeq
What is Addition?
(psupsetq)*(rsupsets)
pveer
:.qvees
What is Constructive Dilemma?
This rule of replacement states the following:
[(p*q)supr]-=[psup(qsupr)]
What is the rule of Exportation?
This rule of replacement states that the following are equivalent:
(pvvq), (qvvp)
(p*q),(p*q)
What is the rule of Commutation?
It decomposes as
p
~q
What is the Negated Conditional or
~(psupsetq)?
It decomposes as
~p
~q
What is the Negated Disjunction or
~(pveeq)?
p*r
:.p
What is Simplification?
p
q
p*q
What is Conjunction?
This rule of replacement states the following:
psupq-=~pvvq
What is the rule of Material Implication/Equivalence?
This rule of replacement states the following:
psupq-=~qsup~p
What is the rule of Transposition?
It decomposes as
/ \
~p ~q
What is the Negated Conjunction or
~(p*q)?
It decomposes as
p
q
What is the Conjunction or
p*q?
pveeq
~p
:.q
What is Disjunctive Syllogism?
psupsetq
qsupsetr
psupsetr
What is Hypothetical Syllogism?
This rule of replacement states the following:
[(pvvq)vvr-=[pvv(qvvr)]
[(p*q)*r-=[p*(q*r)]
What is the rule of Association?
This rule of replacement states the following:
p-=(pvvp), p-=(p*p)
What is the rule of Tautology?
It decomposes as
/ \
p ~p
~q q
What is the Biconditional or
p-=q?
It decomposes as
/ \
p ~p
~q q
What is the Negated Biconditional or
~(p-=q)?
psupsetq
:.psupset(p*q)
What is Absorption?
This rule of replacement states the following:
a(b+c)=(ab+ac)
What is the rule of Distribution?
It decomposes as
/ \
p q
What is the Disjunction or
pveeq?