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20 Cards in this Set
- Front
- Back
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Modus Ponens (M.P) |
p -> q p -------- q |
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Modus Tollens (M.T) |
p -> q ~q --------- ~p |
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Hypothetical Syllogism (H.S) |
p -> q q -> r -------- p -> r |
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Disjunctive Syllogism (D.S) |
p v q ~p ------- q |
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Constructive Dilemma (C.D) |
(p -> q) ^ (r -> s) p v r ---------------------- q v s |
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Destructive Dilemma (D.D) |
(p -> q) ^ (r -> s) ~q v ~s ---------------------- ~p v ~r |
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Simplification (Simp.) |
p ^ q -------- p |
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Conjunction (Conj.) |
p q ---- p ^ q |
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Addition (Add.) |
p -- p v q |
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De Morgan's Theorem (De M.) |
~(p ^ q) = (~p v ~q) ~(p v q) = (~p ^ ~q) |
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Commutation (Com) |
(p v q) = (q v p) (p ^ q) = (q ^ p) |
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Association (Assoc.) |
(p ^ (q ^ r)) = ((p ^ q) ^ r) (p v (q v r)) = ((p v q) v r) |
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Distribution (Dist.) |
(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 (D.N) |
p = ~~p |
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Transposition (Trans.) |
(p -> q) =(~q -> ~p) |
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Material Implication (Impl.) |
p -> q = (~p v q) |
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Material Equivalence (Equiv.) |
(p = q) = ((p -> q) ^ (q -> p)) (p = q) = ((p ^ q) v (~p ^ ~q)) |
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Exportation (Exp.) |
((p ^ q) -> r) = (p -> (q -> r)) |
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Tautology (Taut.) |
p = (p v p) p = (p ^ p) |
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Rule of Excluded Middle |
p v ~p is a tautology p ^ ~p is a contradiction |
