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Let A={1,\ 2,\ 3,\ ,\ 9} and R be the r...

Let `A={1,\ 2,\ 3,\ ,\ 9}` and `R` be the relation on `AxxA` defined by `(a ,\ b)R\ (c ,\ d)` if `a+d=b+c` for all `(a ,\ b),\ (c ,\ d) in AxxA` . Prove that `R` is an equivalence relation and also obtain the equivalence class [(2, 5)].

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The correct Answer is:
`[(2,5)]={(1,4),(2,5),(3,6),(4,7),(5,8),(6,9)}`
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