Prove that the relation `R` on the set `NxxN` defined by `(a ,\ b)R\ lt= gt(c ,\ d) a+d=b+c`

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==== QUESTION TEXT ====

Prove that the relation `R` on the set `NxxN` defined by `(a ,\\ b)R\\ lt = gt (c ,\\ d) a+d=b+c` for all `(a ,\\ b),\\ (c ,\\ d) in NxxN` is an equivalence relation. Also, find the equivalence classes [(2, 3)] and [(1, 3)].

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