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Prove that the relation R on the set Nxx...

Prove that the relation `R` on the set `NxxN` defined by `(a ,\ b)R\ (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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Here, `(a,b)R(c,d) <=> a+d = b+c` for all `(a,b),(c,d) in N xx N.` First we will check `R` for reflexive.
For, `(a,b)R(a,b) `,
`=>a+b = b+a`, which is true.
So, `R` is reflexive.
Now, we will check for symmetric.
...
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