Prove that r is an equivalence relation, Mathematics

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1. Let S be the set of all nonzero real numbers. That is, S = R - {0}. Consider the relation R on S given by xRy iff xy > 0.

(a) Prove that R is an equivalence relation on S, and describe the distinct equivalence classes of R.

(b) Why is the relation R₂ on S given by xR₂y iff xy < 0 NOT an equivalence relation?

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