10.2.19

# 10.2.19 - ∣ x ∣ = ∣ y ∣ Because equality is...

This preview shows page 1. Sign up to view the full content.

INFS 501 10.2.19 Here x A y if and only if xAy x ∣=∣ y . This problem seems hard only because of the formalities using the definitions. Actually, reflexivity, symmetry, and transitivity follow simply from the fact that equality between numbers is reflexive, symmetric, and transitive. Is A Reflexive? Answer : Yes, A is reflexive because x ∈ℝ , x = x , so x A x. Is A Symmetric? Answer : Yes, A is symmtetic, here is why. Suppose x,y ∈ ℝ and x,y  ∈ A, so
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ∣ x ∣ = ∣ y ∣ . Because equality is symmetric, we conclude ∣ y ∣ = ∣ x ∣ and y,x ∈ A, by the definition of A. Is A Transitive? Answer : Yes, A is transitive. Here is why. Suppose x,y,z ∈ ℝ , x,y ∈ A and y,z ∈ A. This means ∣ x ∣=∣ y ∣ and ∣ y ∣=∣ z ∣ . Thu s, ∣ x ∣ = ∣ y ∣ = ∣ z ∣ , so ∣ x ∣ = ∣ z ∣ , making x,z ∈ A by the definition of A....
View Full Document

## This note was uploaded on 11/01/2010 for the course INFS 501 taught by Professor Ellis,w during the Spring '08 term at George Mason.

Ask a homework question - tutors are online