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PredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.1PredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.2PredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.3PPPxPxxPredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.4≥PredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.5LetPxdenotethestatementx3.WhatarethetruthvaluesofP4andP2PredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.6LetQxydenotethestatementxy3.WhatarethetruthvaluesofthepropositionsQ12andQ30PredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.7Rxyz:xyzWhatarethetruthvaluesofthepropositionsR123andR001PredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.8…PredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.9PredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.10PredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.11PredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.122PxuniversalquanificationaPaTTuniversalquantifierPredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.13TheuniversalquantificationofPxisthepropositiondiscourse.”TheuniversalquantificationofPxistheproposition“Pxistrueforallvaluesofxintheuniverseofdiscourse.”PredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.14ExpressthestatementEverystudentinthisclasshasstudiedcalculusasauniversalquantification.ItcanbewrittenasxPxorxSx→PxPxxhasstudiedcalculus.Sxxisinthisclass.PredicatesPredicatesandandQuantifiersQuantifiers8/21/20091:55AMDerenChenZheJiangUniv.15WhatisthetruthvalueofVxPxwherePxisthestatementx10andtheuniverseofdiscourseconsistsofthepositiveintegersnotexceeding4xPxP1P2P3P4.F.PredicatesPredicatesan
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