GenMath Logic Flashcards
Tautology.
[(P v Q) v R) → [P v (Q v R)]
[(P ^ Q) ^ R) → [P ^ (Q ^ R)]
Associative
Tautology.
(P ^ Q) → (Q ^ P)
(P v Q) → (Q v P)
Commutative
Tautology.
[(P v Q) ^ R) → [(P ^ R) v (Q ^ R)]
[(P ^ Q) v R) → [(P v R) ^ (Q v R)}]
Distributive
Tautology.
[(P → Q) ^ (Q → P) ^ (Q → P)] → (P ↔ Q)]
Law of Biconditional Propositions
Tautology.
[P ^ (P → Q)] → Q
Modus Ponens
Tautology.
[(~Q ^ (P → Q)] → ~P
Modus Tollens
Tautology.
[(P ^ Q) → R] → [P → (Q → R)]
Exportation
Tautology.
(P → Q) → (~Q → ~P)
Transposition or Contraposition
Tautology. P → (P v Q)
Addition
Tautology. (P ^ Q) → P
Simplification
Tautology. [(P) ^ (Q)] → (P ^ Q)
Conjunction
Tautology. P → ~(~P)
Double Negation
Tautology. (P → Q) → [P → (P ^ Q)]
Absorption
Tautology. [(P v Q) ^ ~P] → Q
Disjunctive Syllogism
Tautology. (P → Q) → (~P v Q)
Material Implication
Tautology. (P v P) → P
Disjunctive Simplification
Tautology. (P V Q) ^ (~P v R) → (Q v R)
Resolution
Tautology.
[(P → Q) ^ (Q ^ R)] → (P → R)
Hypothetical Syllogism
Tautology.
[(P → Q) ^ (R → S)] ^ (P v R) → (Q v S)
Constructive Dilemma
Tautology.
[(P → Q) ^ (R → S)] ^ (~Q v ~S) → ~P v ~R)
Destructive Dilemma
Valid Arguments.
P → Q
P
———-
∴ Q
Direct Reasoning or Modus Ponens
Valid Arguments.
P → Q
~Q
———-
∴ ~P
Contrapositive Reasoning or Modus Tolens
Valid Arguments.
P v Q ____________ P v Q
~P ________________~Q
——- ____________———–
∴ Q_______________ ∴ P
Disjunctive Reasoning or Disjunctive Syllogism
Valid Arguments.
P → Q
Q → R
————–
∴ P → R
~R → ~P
Transitive Reasoning or Hypothetical Syllogism
Fallacy.
P → Q
Q
————
∴ P
Fallacy of the Converse
Fallacy.
P → Q
~P
———–
∴ ~Q
Fallacy of the Inverse
Fallacy.
P v Q ________________ P v Q
P ____________________ Q
———— ____________ ————-
∴ ~Q _________________ ∴ ~P
Misuse of Disjunctive Reasoning
Fallacy.
P → Q
Q → R
———————-
∴ R → P
~P → ~R
Misuse of Transitive Reasoning
