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## Homework Statement

We define a relation

**~**for

**N^**2 by:

**(n, m) ~(k, l) <=> n + l = m + k**

Show that

**~**is a equivalence relation

## Homework Equations

A relation R on a set A is equivalent if R is:

**reflexive**if x R x for all x that is an element of A

**symmetric**if x R y implies y R x, for all x,y that is an element of A

**transitive**if x R y and y R z imply x R z, for all x,y,z that is an element of A

## The Attempt at a Solution

I have to prove this by showing that the relation is reflexive, symmetric and transitive. The symmetric part i understand, the fact that we can turn the relation around and it will be the same: n + l = m + k

**vs**m + k = n + l.

But how do I prove the refexive and transitive part? I am really confused by the ~ and do not quite understand why it appears both as the name of the relation and as an element of the relation itself.