Transcription of Discrete Mathematics, Chapter 1.4-1.5: Predicate Logic
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Discrete Mathematics, Chapter 1.4-1.5: Predicate Logic
Discrete Mathematics, Chapter : Predicate LogicRichard MayrUniversity of Edinburgh, UKRichard Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter / 23 Outline1 Predicates2 Quantifiers3 Equivalences4 Nested QuantifiersRichard Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter / 23 Propositional Logic is not enoughSuppose we have: All men are mortal. Socrates is a man .Does it follow that Socrates is mortal ?This cannot be expressed in propositional need a language to talk about objects, their properties and Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter / 23 Predicate LogicExtend propositional Logic by the following new :x,y,z,.. predicates ( , propositional functions):P(x),Q(x),R(y),M(x,y).
Statements involving predicates and quantifiers are logically equivalent if and only if they have the same truth value for every predicate substituted into these statements and for every domain of discourse used for the variables in the expressions. The notation S T indicates that S and T are logically equivalent. Example: 8x ::S(x) 8x S(x).
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