{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

problems12-sol - MATH S-104 Lecture 12 In-class Problem...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH S-104 Lecture 12 In-class Problem Solutions July 30, 2009 Problem 1 * : Which of these relations on the set of all functions from Z to Z are equivalence relations? Determine the properties of an equivalence relation that the others lack. a) {( f,g ) f ( 1 ) = g ( 1 )} i. reflexive: a function always equals itself ii. symmetric: if f ( ) = g ( ) , then g ( ) = f ( ) iii. transitive: if f ( ) = g ( ) and g ( ) = h ( ) , then f ( ) = h ( ) b) {( f,g ) f ( ) = g ( ) or f ( 1 ) = g ( 1 )} i. reflexive: yes ii. symmetric: yes iii. transitive: no. What if f ( ) = g ( ) and g ( 1 ) = h ( 1 ) . It could be the case that f ( ) ≠ h ( ) and f ( 1 ) ≠ h ( 1 ) . c) {( f,g ) f ( x )- g ( x ) = 1for all x ∈ Z } i. reflexive: no. f ( x )- f ( x ) = ii. symmetric: no. f ( x )- g ( x ) = 1 means that g ( x )- f ( x ) =- 1 iii. transitive: no. If f ( x )- g ( x ) = 1 and g ( x )- h ( x ) = 1, then f ( x )- h ( x ) = 2....
View Full Document

{[ snackBarMessage ]}

Page1 / 3

problems12-sol - MATH S-104 Lecture 12 In-class Problem...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online