Is (x,y)<(j,k) Defined as an Order Relation by x+k<y+j?

[dpa]

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?

 

[sammycaps]

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 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.