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Propositional Function - Discrete Mathematics - Lecture Slides

Slides, Discrete Mathematics

Post: April 27th, 2013
Description
During the study of discrete mathematics, I found this course very informative and applicable.The main points in these lecture slides are:Propositional Function, Nested Quantifiers, Rules of Inference, Universe of Discourse, Quantified Predicates, Quantified Variables, Existential Quantifier, Universal Quantifier, Predicate Logic and Propositions
During the study of discrete mathematics, I found this course very informative and applicable.The main points in these lecture slides are:Propositional Function, Nested Quantifiers, Rules of Inference, Universe of Discourse, Quantified Predicates, Quantified Variables, Existential Quantifier, Universal Quantifier, Predicate Logic and Propositions
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Contents
Discrete Mathematics CS 2610 August 21, 2008 Docsity.com Agenda Nested quantifiers Rules of inference Proofs 2 Docsity.com Review A predicate P, or propositional function, is a function that maps objects in the universe of discourse to propositions Predicates can be quantified using the universal quantifier (“for all”) ∀ or the existential quantifier (“there exists”) ∃ Quantified predicates can be negated as follows   ¬∀x P(x) ≡ ∃x ¬P(x) ¬∃x P(x) ≡ ∀x ¬P(x) Quantified variables are called “bound” Variables that are not quantified are called “free” 3 Docsity.com Predicate Logic and Propositions An expression with zero free variables is an actual proposition Ex. Q(x) : x > 0, R(y): y < 10 ∃ x Q(x) ∧ ∃y R(y) 4 Docsity.com Nested Quantifiers When dealing with polyadic predicates, each argument may be quantified with its own quantifier. Each nested quantifier occurs in the scope of another quantifier. Examples: (L=likes, UoD(x)=ki..

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