PPT-Defn: A relation is a set of ordered pairs.

Domain The x values of the ordered pair Range The y values of the ordered pair 35 Introduction to Functions x y 1 3 2 5 4 6 1 4 3 3 x y 4 2 3 8 6 1 1 9 5 6 x. Chapter 9. 1. Chapter Summary. Relations and Their Properties. n. -. ary. Relations and Their Applications (. not currently included in overheads. ). Representing Relations. Closures of Relations (. CMPS 2433- Chapter 2. Partially borrowed from Florida State . University and . Dr.. R Halverson. Introduction. A . set. is a collection of objects. The order of the elements does not matter. Objects in a set are called . Selected Exercises. Goals. . Introduce . big-O . & big. -. Omega. S. how . how . to estimate . the size of functions using this notation.. Copyright © Peter . Cappello. 2. Preface. You may use . Coordinate system. : used to locate points . also call the Coordinate plane. Origin. : is a (0,0) and is the point at which the number lines intersect. X-Axis. : the horizontal number line. Y-Axis. : the vertical number line. Selected Exercises. Partial Order. Let R be a relation on A.. R is a . partial order . when it is:. Reflexive. Antisymmetric. Transitive.. Copyright © Peter Cappello. 2. Copyright © Peter . Cappello. Relations . & Functions. After today’s lesson, you should be able to:. Explain the difference between a relation and a function. Identify whether a relation is a function. Identify the domain and range of a relation or a function. Objective:. To graph relations. To identify functions. Relations. A relation is a set of pairs of input and output values.. You can write a relation as a set of ordered pairs.. Graphing Relations. To graph relations, plot the points. . Section 9.3. Representing Relations Using Matrices. A relation between finite sets can be represented using a zero-one matrix. . Suppose . R. is a relation from . A. = {. a. 1. , . a. 2. , …, . a. on . your . homework. .. 1.To make 5 apple pies, you need 2 pounds of apples. How many pounds of apples do you need to make 20 pies? . 2. Four balls of wool will make 8 knitted caps. How many balls of wool will it take to make 6 caps? . Presented By: Andrew F. Conn. Lecture #22: Relations and Representations. November 28. th. , 2016. Binary relations establish a relationship between elements of two sets. Definition: . Let . and . be two sets. A . A function maps each element in the domain to exactly 1 element in the range. . Concept 1. Example 1. Domain and Range. State the domain and range of the relation. Then determine whether the relation is a function. If it is a function, determine if it is . Section. . 2.2. Relations. In symbols . we have (. a. , . b. ) = . {. {. a. }, {. Objectives: Determine whether a relation is a function, identify the domain and range, evaluate functions. Relation:. A set of ordered pairs. Domain (D):. The first element in an ordered pair. (abscissa). The objects of mathematics may be . related. in various ways. . A set . A. may be said to be “related to” a set . B. if . A. is a subset of . B. , or if . A. is not a subset of . B. , or if .