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1-001 Logic University abbreviation ambiguous answer argument form argument is valid Argumentum Aristotle biconditional Chapter conclusion false Consider Construct a truth Contrafactum counter-example deductively valid argument defined definite description Denying the Antecedent employ English sentences example F F F F T F F fallacy Fallacy of Composition finished tree following argument form following sentences formula Hominem horse identical imply impossible inconsistent inductively interpretation invalid logical truth logically equivalent logician Minnesota Professor John Modus Ponens Modus Tollens mutually consistent negation open path person philosophers Philosophy 1-001 Logic planets predicate logic premises are true proposition quantifier question reasoning sentences are mutually sentential connective sentential letters set of sentences Socrates Solutions someone Specimen Fifty-Minute Exam symbolize table to determine tautology term tree rules tree shows tree to determine truth functional truth table truth tree truth value truth-functional Universe of Discourse words write possible x)Fx x)Fxy y)Fxy