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CSE 20 DISCRETE MATH Prof. Shachar Lovett http://cseweb.ucsd.edu/classes/wi15/cse20-a/ Clicker frequency: CA

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Todays topics Relations Section 6.1 in Jenkyns, Stephenson

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(Binary) Relations

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Relations are graphs Think of relations as directed graphs U=nodes of graphs xRy means “there in an edge x y” Is A. R ? B. R ? C. Both D. Neither

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Relations are graphs What does this relation captures? xRy means A. x>y B. x=y C. x divides y D. x+y E. None/more than one 2 3 4 1 5 6

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Three important properties of relations

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Symmetric relations

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Types of relations

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Test your understanding

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Let U=“all Boolean formulas on n inputs” xRy = “x and y compute the same Boolean function” Is R symmetric / reflexive / transitive? A. Yes,Yes,Yes B. No,No,No C. Yes,Yes,No D. No,No,Yes E. Other

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Next class Equivalence relations Read section 6.2 in Jenkyns, Stephenson

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Section 9.3. Section Summary Representing Relations using Matrices Representing Relations using Digraphs.

Section 9.3. Section Summary Representing Relations using Matrices Representing Relations using Digraphs.

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