Hmk4 - COT 3100 Homework # 4 Spring 2000 Assigned: 3/7/00...

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

View Full Document Right Arrow Icon
COT 3100 Homework # 4 Spring 2000 Assigned: 3/7/00 Due: 3/30,31 in recitation 1) Define a relation T N x N such that T = {(a,b)| a A b A a – b = 2c+1 for some integer c}. (N is the set of non-negative integers.) a) Prove that this relation is not reflexive. b) Prove that this relation is symmetric. c) Define the term anti-transitive as the following: Given a set A and a relation R, if for all a,b,c A, (aRb bRc cRa) (a = b b = c) Prove that the relation T is anti-transitive. 2) Let g: A A be a bijection. For n 2, define g n = g ° g ° ... ° g, where g is composed with itself n times. Prove that for n 2, that g n is a bijection from A to A as well, and show that (g n ) -1 = (g -1 ) n . 3) Let f : A B and g: B C denote two functions. If both f and g are injective, prove that the composition g ° f: A C is an injection as well. 4)
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 07/14/2011.

Page1 / 2

Hmk4 - COT 3100 Homework # 4 Spring 2000 Assigned: 3/7/00...

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