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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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(i) Reflexivity

`\operatorname{Let}(a, b) \in A \times A`, then

`(a, b) \in A \times A \Rightarrow a, b \in A`

`\Rightarrow a+b=b+a`

...
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