# 09-TautolContradic - Discussion #9 Tautologies and...

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Discussion #9 Chapter 1, Section 4 1/16 Discussion #9 Tautologies and Contradictions

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Discussion #9 Chapter 1, Section 4 2/16 Topics Definitions Sound reasoning with tautologies and contradictions Logical equivalences: By truth table and reductions ¬ , , and reductions
Discussion #9 Chapter 1, Section 4 3/16 Definitions Tautology – a logical expression that is true for all variable assignments. The symbol |= (read “entails”) denotes that what follows holds or is true, so long as what precedes it is true. Since tautologies are always true, we sometimes write “|= B” to denote that B is a tautology independent of what precedes it. Contradiction – a logical expression that is false for all variable assignments. Contingent – a logical expression that is neither a tautology nor a contradiction.

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Discussion #9 Chapter 1, Section 4 4/16 Tautologies F F T T T F F T ¬ (P ¬ P) P ¬ P ¬ P P T T T T T T T F F F F T F F T F F T T T ¬ (P Q) Q ¬ (P Q) P Q Q P P ¬ P is a tautology, |= P ¬ P.
Discussion #9 Chapter 1, Section 4 5/16 Tautological Derivation by Substitution Since |= A ¬ A, so is |= (P Q) ¬ (P Q) and |= (P

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## This note was uploaded on 03/02/2012 for the course C S 236 taught by Professor Michaelgoodrich during the Winter '12 term at BYU.

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09-TautolContradic - Discussion #9 Tautologies and...

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