Unformatted text preview: 1. If h is onetoone, then either f or g must be onetoone 2. If h is a bijection, then both f and g must be surjective Problem 3 (9 points) For each of the following relations, determine if it is an equivalence relation. If so, list its equivalence classes. If not, says which properties (reﬂexive, symmetric and transitive) it fails to satisfy. (If it fails more than one property, list all of them.) 1. The relation R on { 1 , 2 , 3 , 4 , 5 , 6 } deﬁned by aRb ≡ 2  ( a + b ) , i.e., ( a,b ) is in the relation if a + b is even 2. The relation R on the powerset 2 { 1 , 2 , 3 } where ( A,B ) ∈ R if and only if A ∩ B = ∅ 3. The relation R on the set { 1 , 2 , 3 , 4 , 5 , 6 } deﬁned by aRb ≡ 3  ( a + b )...
View
Full
Document
This note was uploaded on 01/08/2011 for the course CSE cse105 taught by Professor Cs during the Fall '10 term at UCSD.
 Fall '10
 CS

Click to edit the document details