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Let S be a relation on the set R of al...

Let `S` be a relation on the set `R` of all real numbers defined by `S={(a , b)RxxR: a^2+b^2=1}dot` Prove that `S` is not an equivalence relation on `Rdot`

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We observe the following properties of `{S}`.

Reflexivity:

Let `a` be an arbitrary element of `R`. Then,

`a in R `

`Rightarrow a^{2}+a^{2} neq 1 forall z in R`

`Rightarrow(a, a) notin S`

`{So}_{,} {S}` is not reflexive on `{R}`.

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