UCF COT 3100 - Intro to Discrete Structures (25 pages)

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Intro to Discrete Structures



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Intro to Discrete Structures

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Pages:
25
School:
University of Central Florida
Course:
Cot 3100 - Introduction to Discrete Structures
Introduction to Discrete Structures Documents

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Intro to Discrete Structures Lecture 5 Pawel M Wocjan School of Electrical Engineering and Computer Science University of Central Florida wocjan eecs ucf edu Intro to Discrete StructuresLecture 5 p 1 25 Office Hours Tuesday 2 45pm 4 00pm Thursday 1 00pm 2 15pm Intro to Discrete StructuresLecture 5 p 2 25 Nested Quantifiers Two quantifiers are nested if one is within the scope of the other such as x y x y 0 Everything within the scope of a quantifier can be thought of as a propositional function Define the propositional functions Q x yP x y P x y x y 0 Then we have x y x y 0 x yP x y xQ x Intro to Discrete StructuresLecture 5 p 3 25 Thinking of Quantification as Loops In working with quantification of more than one variable it is sometimes helpful to think in terms of nested loops Of course if there are infinitely many elements in the domain of some variable we cannot actually loop through all values Nevertheless this way of thinking is helpful in understanding nested quantifiers For example x yP x y corresponds to for x do for y do if P x y return F end for end for return T Intro to Discrete StructuresLecture 5 p 4 25 Thinking of Quantification as Loops For example x yP x y corresponds to for x do temp F for y do if P x y then temp T break end for if temp return F end for return T Intro to Discrete StructuresLecture 5 p 5 25 Order of Quantifiers x yP x y y xP x y True if P x y is T for every pair x y False if there is a pair x y for which P x y is F x yP x y y xP x y True if there is a pair x y for which P x y is T False if P x y is F for every pair x y Intro to Discrete StructuresLecture 5 p 6 25 Order of Quantifiers x yP x y True if for every x there is a y for which P x y is T False if there is an x such that P x y is F for every y x yP x y True if there is an x for which P x y is T for every y False if for every x there is a y for which P x y is F Intro to Discrete StructuresLecture 5 p 7 25 Reading Assignment Translating Mathematical Statements into Statements



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