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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) 