a1-31-08

a1-31-08 - Answers to Homework 31 January 2008 13.1...

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 DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Answers to Homework 31 January 2008 13.1 Relations on A = f 1 ; 2 ; 3 ; 4 ; 5 g . (a) f (1 ; 1) ; (2 ; 2) ; (3 ; 3) ; (4 ; 4) ; (5 ; 5) g is the equality relation. It is re&ex- ive, symmetric, antisymetric and transitive. (b) f (1 ; 2) ; (2 ; 3) ; (3 ; 4) ; (4 ; 5) g is the relation given by the equation y = x + 1 . It is irre&exive and antisymmetric. (c) f (1 ; 1) ; (1 ; 2) ; (1 ; 3) ; (1 ; 4) ; (1 ; 5) g is the relation given by the equation x = 1 . It is antisymmetric and transitive. (d) f (1 ; 1) ; (1 ; 2) ; (2 ; 1) ; (3 ; 4) ; (4 ; 3) g is symmetric. (e) f 1 ; 2 ; 3 ; 4 ; 5 g & f 1 ; 2 ; 3 ; 4 ; 5 g is re&exive, symmetric, and transitive. 13.2 R is a relation on the set Z of integers: xRy if x and y di/er by at most 2 . (a) R = f ( x;y ) : x and y are in Z , and j x ¡ y j ¢ 2 g . (b) R is re&exive because j x ¡ x j = 0 ¢ 2 for all integers x . (c) R is not irre&exive because, for example, j 3 ¡ 3 j = 0 ¢ 2 ....
View Full Document

This note was uploaded on 07/13/2011 for the course MAD 2104 taught by Professor Staff during the Spring '08 term at FAU.

Page1 / 2

a1-31-08 - Answers to Homework 31 January 2008 13.1...

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

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