MA112-Lecture_Notes-OH-L04

# MA112-Lecture_Notes-OH-L04 - MA112 Discrete Mathematics...

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MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 1 MA112 Discrete Mathematics Omar Hamdy [email protected] Lecture Notes 4

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MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 2 Review: Predicate Logic • Propositions do not have centric meanings. They cannot generalize facts. • Predicate Logic explicitly models objects and their attributes. • Allows to build statements with variables. • Allows to build statements for group of objects. • When applying a predicate to a variable subject denoted by P(x), we obtain a propositional function.
MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 3 Review: Quantifiers • Predicate logic gives the ability to make a statement about groups of subjects. • These are called quantified statements • There are two types of quantifiers: – Universal: , reads for all • All engineers have engineering degree – Existential: , reads there exists • Some engineers have double majors

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MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 4 Review: Quantifiers Def: The universal quantification of P(x) is the proposition “P(x) is true for all values of x in the universe of discourse”. Def: The existential quantification of P(x) is the proposition “There exists and element in the universe of discourse such that P(x) is true”.
MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 5 Quantification Summary • Quantification converts a propositional function into a proposition by substituting variables with values from the universe of discourse. P(x) is false for all x. There is some x for which P(x) is true x P(x) There is an x where P(x) is false P(x) true for all x x P(x) When False? When True? Statement

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MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 6 Nested Quantifiers • Nested quantifiers is sometimes necessary to capture the relations and meanings of predicate logic statements. There is an animal which is faster than all
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## This note was uploaded on 01/06/2011 for the course MA 112 taught by Professor Omarhamdy during the Spring '10 term at Helwan University, Helwan.

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MA112-Lecture_Notes-OH-L04 - MA112 Discrete Mathematics...

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