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21 Cards in this Set

  • Front
  • Back
disjunctive syllogism
(DS) - valid

p v q
~p
-----------
q
pure hypothetical syllogism
(HS) - valid

p>q
q>r
--------
p>r
modus ponens
(MP) - valid

p>q
p
------
q
modus tollens
(MT) - valid

p>q
~q
-------
~p
affirming the consequent
(AC) - invalid

p>q
q
-------
p
denying the antecedent
(DA) - invalid

p>q
~p
------
~q
constructive dilemma
(CD) - valid

(p>q) . (r>s)
p v r
----------
q v s
destructive dilemma
(DD) - valid

(p>q) . (r>s)
~q v ~s
------------------
~p v ~r
conjunction
(Conj)

p
q
-----
p . q
simplification
(Simp)

p . q
-------
p
addition
(Add)

p
------
p v q
de morgan's rule
(DM)

~(p . q) :: (~p v ~q)
~(p v q) :: (~p . ~q)
commutativity
(Com)

(p v q) :: (q v p)
(p . q) :: (q . p)
associativity
[p v (q v r)] :: [(p v q) v r]
[p . (q . r)] :: [(p . q) . r]
distribution
[p . (q v r)] :: [(p . q) v (p . r)]
[p v (q . r)] :: [(p v q) . (p v r)]
double negation
p:: ~~p
transportation
(p>q) :: (~q>~p)
material implication
(Impl)

(p>q) :: (~p v q)
material equivalence
(p=q) :: [(p>q) . (q>p)]
(p=q) :: [(p . q) v (~p . ~q)]
exportation
[(p . q)>r] :: [p>(q>r)]
tautology
p :: (p v p)
p :: (p . p)