# Defining order relation

## Homework Statement

Q. Define an order relation
(x,y)<(j,k) if and only if x+k<y+j

## Homework Equations

x<y means x+a=y and viceversa

## The Attempt at a Solution

I have no idea. To show it is equivalence relation, I simply show that it is reflexive, transitive and symmetric. but how do I show it is order relation?

## Answers and Replies

Order Relation (call it C)
1) For every x and y, with x not equal to y, xCy or yCx
2) xCx is never true
3) xCy, yCz implies xCz

HallsofIvy
Homework Helper

## Homework Statement

Q. Define an order relation
(x,y)<(j,k) if and only if x+k<y+j

## Homework Equations

x<y means x+a=y and viceversa
With a> 0, of course.

## The Attempt at a Solution

I have no idea. To show it is equivalence relation, I simply show that it is reflexive, transitive and symmetric. but how do I show it is order relation?
An order relation only has to be transitive.