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26 Cards in this Set
- Front
- Back
tautology |
statements that are always true for every line of the truth table |
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contradiction |
a statement that is false for every line of the truth table |
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contingent |
a statement with mixed truth values |
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logically equivalent |
they have the same truth values for every line of the truth table |
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logically contradictory |
they have opposite truth values on every line of the truth table |
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logically inconsistent |
there is no row of the truth table in which both statements are true |
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modus ponens |
p--> q p, so q |
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modus tolens |
p--> q ~q, so ~ p |
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disjunctive syllogism |
p v q ~p, so q or ~q, so p |
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simplication |
p*q so p, or so q |
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conjunction |
if p and if q, then p*q |
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hypothetical syllogism |
p-->q, q-->r, so p-->r |
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addition |
if p is true, then p v (any variable) is true |
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constructive dilemma |
pvq p--> r q-->s so, rvs |
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double negation |
p:: ~~p |
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commutation |
(pvq) :: (qvp) (p*q) ::(q*p) |
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association |
pv (qvr) :: (pvq) vr p*(q*r) :: (p*q)*r |
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DeMorgan's Law |
~(pvq) :: (~pv~q) ~(p*q) :: (~p*~q) |
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contraposition |
p-->q :: ~q-->~p |
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distribution |
(p*[qvr]) :: (p*q) v (p*r) (pv[q*r]) :: (pvq) * (pvr) |
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exportation |
(p*q)-->r :: p--> (q-->r) |
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redundancy |
p*p :: p pvp :: p |
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material equivalence |
p<-->q :: (p*q) v (~p*~q) (either they are both true, or neither are true) p<-->q :: (p-->q) * (q-->p) |
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material implication |
(p-->q) :: ~pvq (either p is not true, or q istrue |
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conditional proof |
conclusion must be a conditional, biconditional, or a disjunct that can be made into a conditional (assume that the antecedent of the conclusion is true, and solve) |
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indirect proof |
assume conclusion is false, and find the contradiction in the premises (if there is a contradiction, then it is wrong to assume the conclusion is false) |