CSE 20 DISCRETE MATH Prof. Shachar Lovett Clicker frequency: CA

Todays topics Relations Section 6.1 in Jenkyns, Stephenson

(Binary) Relations

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

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

Three important properties of relations

Symmetric relations

Types of relations

Test your understanding

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

Next class Equivalence relations Read section 6.2 in Jenkyns, Stephenson