Abstract Algebra: Theory and Applications · Problem 1.14

Preliminaries — Thomas Judson

Mathematics — Abstract Algebra · equivalence-relations

Problem

Define a relation on

\mathbb{R}^2

by stating that

(a, b) \sim (c, d)

if and only if

a^2 + b^2 \leq c^2 + d^2

. Show that

\sim

is reflexive and transitive but not symmetric.