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21 Cards in this Set
- Front
- Back
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disjunctive syllogism
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(DS) - valid
p v q ~p ----------- q |
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pure hypothetical syllogism
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(HS) - valid
p>q q>r -------- p>r |
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modus ponens
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(MP) - valid
p>q p ------ q |
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modus tollens
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(MT) - valid
p>q ~q ------- ~p |
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affirming the consequent
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(AC) - invalid
p>q q ------- p |
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denying the antecedent
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(DA) - invalid
p>q ~p ------ ~q |
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constructive dilemma
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(CD) - valid
(p>q) . (r>s) p v r ---------- q v s |
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destructive dilemma
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(DD) - valid
(p>q) . (r>s) ~q v ~s ------------------ ~p v ~r |
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conjunction
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(Conj)
p q ----- p . q |
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simplification
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(Simp)
p . q ------- p |
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addition
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(Add)
p ------ p v q |
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de morgan's rule
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(DM)
~(p . q) :: (~p v ~q) ~(p v q) :: (~p . ~q) |
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commutativity
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(Com)
(p v q) :: (q v p) (p . q) :: (q . p) |
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associativity
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[p v (q v r)] :: [(p v q) v r]
[p . (q . r)] :: [(p . q) . r] |
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distribution
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[p . (q v r)] :: [(p . q) v (p . r)]
[p v (q . r)] :: [(p v q) . (p v r)] |
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double negation
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p:: ~~p
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transportation
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(p>q) :: (~q>~p)
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material implication
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(Impl)
(p>q) :: (~p v q) |
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material equivalence
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(p=q) :: [(p>q) . (q>p)]
(p=q) :: [(p . q) v (~p . ~q)] |
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exportation
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[(p . q)>r] :: [p>(q>r)]
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tautology
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p :: (p v p)
p :: (p . p) |
