This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: R or by describing the property that relates the two elements. Example 3.1 Let A = { 1 , 2 , 3 } and B = { a, 5 , { b } ,c } and R be given by R = { (1 ,a ) , (1 ,b ) , (2 ,a ) , (2 ,c ) } . Then • we have 1 Ra , 1 R { b } , 2 Ra , 2 Rc , 3 6 R 5 • Dom ( R ) = { 1 , 2 } ⊆ A • Rng ( R ) = { a, { b } ,c } ⊆ B Example 3.2 Let P be the set of all people. Let L = { ( a,b ) ∈ P × P  a and b have the same last name } . Then L is a relation on P . Example 3.3 Let S be a relation on the set N × N deﬁned by ( m,n ) S ( k,j ) iﬀ m + n = k + j . Then (3 , 17) S (12 , 8) but (5 , 4) 6 S (6 , 15) . Note that we can write S as S = { (( m,n ) , ( k,j )) ∈ N 2 × N 2  m + n = k + j } . What are the domain and range of S ? 2...
View
Full
Document
This note was uploaded on 01/25/2010 for the course MATH 21127 taught by Professor Howard during the Spring '08 term at Carnegie Mellon.
 Spring '08
 howard
 Math, Set Theory, Sets

Click to edit the document details