(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

We define a relation~forN^2 by:

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

Show that~is a equivalence relation

2. Relevant equations

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

reflexiveif x R x for all x that is an element of A

symmetricif x R y implies y R x, for all x,y that is an element of A

transitiveif x R y and y R z imply x R z, for all x,y,z that is an element of A

3. 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 + kvsm + 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.

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# Homework Help: Equivalence relation

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