3 laws of logic - Discrete Mathematics Laws of Logic 4-2...

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1IntroductionLaws of LogicDiscrete MathematicsAndrei BulatovDiscrete Mathematics – Laws of Logic4-2Previous LectureTruth tablesTautologies and contradictionsLogic equivalencesDiscrete Mathematics – Laws of Logic4-3Logic EquivalencesCompound statementsΦandΨare said to belogicallyequivalentif the statementΦis true (false) if and only ifΨistrue (respectively, false)orThe truth tables ofΦandΨare equalorFor any choice of truth values of the primitive statements(propositional variables) ofΦandΨ,formulasΦandΨhavethe same truth valueIfΦandΨare logically equivalent, we writeΦ ⇔ ΨDiscrete Mathematics – Laws of Logic4-4Why Logic EquivalencesTo simplify compound statements``If you are a computer science major or a freshman and you arenot a computer science major or you are granted access to theInternet, then you are a freshman or have access to the Internet’’To convert complicated compound statements to certain `normalform’ that is easier to handleConjunctive Normal FormCNFDiscrete Mathematics – Laws of Logic4-5Example Equivalences

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Term
Spring
Professor
AndreiBulatov

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