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### 49 Cards in this Set

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 A Proposition a declarative sentence (a sentence that declares a fact) that is either true or false, but not both Propositional variables or statement variables variables that represent propositions, just as letters are used to denote numerical variables Truth Table: P^Q Only both TFFF ~P^Q P^~Q Only one and not the other FFTF FTFF ~P^~Q Only not one and not the other FFFT equivalent to ~(PvQ) ~(P^Q) Not both, but anything else FTTT equivalent to ~Pv~Q PvQ Everything except both false TTTF ~PvQ Pv~Q Anything except one but not the other TFTT (equivalent to P→Q) TTFT (equivalent to Q→P) ~Pv~Q Anything except both true FTTT ~(PvQ) Not one or the other, therefore only neither FFFT equivalent ~P^~Q Truth tables and intuitive meaning P→Q Anything except P=T Q=F TFTT Equivalent (~PvQ) not the case of one and not the other Truth tables and intuitive meaning ~P→Q Anything except both false TTTF equivalent (PvQ) Truth tables and intuitive meaning P→~Q Anything except both true FTTT Truth tables and intuitive meaning ~P→~Q Anything except P=F and Q=T TTFT Truth tables and intuitive meaning ~(P→Q) Only the case where P is true and Q is false FTFF equivalent (P^~Q) Equivalence P^T P^F Identity laws P Equivalence PvT PvF Domination Laws T F Equivalence PvP P^P Idempotent laws P Equivalence PvQ P^Q Commutative QvP Q^P Equivalence Pv(Q^R) P^(QvR) Distributive (PvQ)^(PvR) (P^Q)v(P^R) equivalence (PvQ)^(PvR) (P^Q)v(P^R) reverse of distributive law Pv(Q^R) P^(QvR) Equivalence ~(P^Q) ~(PvQ) De Morgan's ~Pv~Q ~P^~Q Equivalence ~Pv~Q ~P^~Q reverse of De Morgan's ~(P^Q) ~(PvQ) Equivalence Pv(P^Q) P^(PvQ) Absorption P Equivalence ~(P→~Q) P^Q Equivalent Conditional PvQ ~P→Q Equivalence ~(P→Q) P^~Q Equivalence (P→Q)^(P→R) P→(Q^R) Equivalence P→(Q^R) (P→Q)^(P→R) Equivalence (P→R)^(Q→R) (PvQ)→R Equivalence (PvQ)→R (P→R)^(Q→R) Equivalence (P→Q)v(P→R) P→(QvR) Equivalence P→(QvR) (P→Q)v(P→R) Equivalence (P→R)v(Q→R) (P^Q)→R Equivalence (P^Q)→R (P→R)v(Q→R) Equivalence P↔Q Three total (P→Q)^(Q→P) ~P↔~Q (P^Q)v(~P^~Q) Equivalence ~(P↔Q) 2 total P↔~Q ~(P^Q)^(PvQ) Inference Rule P P→Q → Modus Ponens Q Inference Rule ~Q P→Q → Modus Tollens ~P Inference Rule P→Q Q→R → Hypothetical Syllogism P→Q Inference Rule PvQ ~P → Disjunctive Syllogism Q Inference Rule P → Addition PvQ Inference Rule P^Q → Simplification P Inference Rule P Q → Conjunction P^Q Inference Rule PvQ ~PvR → Resolution QvR Inference Rule ∀xP(x) → Universal instantiation P(c) Inference Rule P(c) for an arbitrary c → Universal Generalization ∀xP(x) Inference Rule ∃xP(x) → Exitential instantiation P(c) for some element c Inference Rule P(c) for some element c → Existential generalization ∃xP(x)