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Operator Name Logical function Words to translate ~ Tilde’ Negation Not, it’s not the case (negate) or but . Dot Conjunction And, also, moreover, but (combine 2 prop) v Wedge Disjunction Either/or, unless ⊃ Horseshoe Implication If then, only if (antecedent/consequent) ≡ Triple bar Equivalence If and only if 1. Negation/Tilde P ~P T F F T -It is not the case that… A Ex. ~A 2. Conjunction/ dot P Q P.Q T T T T F F F T F F F F - And, but etc Ex. D.C 3. Disjunction/Wedge P Q PvQ T T T T F T F T T F F F -true, unless both disjuncts are false a. inclusive disjunction- Either A or B or both (AvB) b. exclusive disjunction- Either/or but not both 4. Material Implication/ Conditional/horseshoe P Q P ⊃Q T T T T F F F T T F F T -true, unless antecedent is true and consequent is false. -Ex: if P then Q= P ⊃Q 5. Equivalence/triple bar P Q P ≡Q T T T T F F F T F F F T - True, if both are true and both are false (same truth value)

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OperatorNameLogical functionWords to translate

~TildeNegationNot, its not the case (negate) or but

.DotConjunction And, also, moreover, but (combine 2 prop)

vWedgeDisjunctionEither/or, unless

HorseshoeImplicationIf then, only if (antecedent/consequent)

Triple barEquivalenceIf and only if

1. Negation/TildeP~P

TF

FT

-It is not the case that A Ex. ~A2. Conjunction/ dotPQP.Q

TTT

TFF

FTF

FFF

And, but etc Ex. D.C3. Disjunction/WedgePQPvQ

TTT

TFT

FTT

FFF

-true, unless both disjuncts are falsea. inclusive disjunction- Either A or B or both (AvB)b. exclusive disjunction- Either/or but not both

4. Material Implication/ Conditional/horseshoePQPQ

TTT

TFF

FTT

FFT

-true, unless antecedent is true and consequent is false.-Ex: if P then Q= PQ

5. Equivalence/triple barPQPQ

TTT

TFF

FTF

FFT

True, if both are true and both are false (same truth value)


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