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Functional completenessIf and only ifInclusive orTruth valueLogical biconditionalConjunction introductionBoolean functionLogical connectiveAxiomatic systemBoolean algebraFormal languageUniversal quantifierConjunctionAxiom of unionPrinciple of compositionalityClassical logicImplicationIntersectionConverseAlgebra of setsPropositional logicTruth functionConjunctive normal formTruth tableLogical consequenceClassLogical norAxiom of pairingExtensionalitySubsetCartesian productConditional proofTautologyTransitive setGroupDisjunctionQuantifierProof systemValuationStrict conditionalExclusive orExistential theory of the realsAxiom of extensionalityPropositional variableExistential quantifierProof by contradictionSymbolic logicExtensionSyllogismPropositional functionAlgebraFirst-order logicPrinciple of bivalenceTransitive relationInclusion functionRule of inferenceFormulaEquationBoolean logicNecessity and sufficiencyInclusion mapInference ruleAlgebraic structureElementary equivalenceCategorical propositionLogical equivalenceSet-builder notationConnectionDisjunctive normal formSatisfiabilityTruth treeCountable additivityLöb's theoremUnconditionalUnionRecursive languageMathematical structureMathematical logicDouble negationExpressionOperator associativityClauseSymmetric differenceAlgebraic expressionPredicate calculusClosureTheoremClosure operatorLaw of excluded middleBiconditionalLogicSyntaxIncidence algebraOperadArithmetic operatorSet theoryAxiom of regularityFieldBoolean domainPropositional formula