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Equivalence Relation

9.Let S be th...

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9.Let S be the set of all real numbers and let R ={(a, b) :a, b belongs to S and a=+-b}. Show that R is an equivalence relation on S.

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Q. Let S be a relation on the set R of all real numbers defined by
S = {(a, b) ∈ R × R : a² + b² = 1}
Prove that S is not an equivalence relation on R.

Q. Let S be the set of all real numbers and let R be a relation on S, defined by a R b

\Leftrightarrow

\leq

Q. Let S be the set of all real numbers and let R be a relation on S, defined by a R b

\Leftrightarrow

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be the set of all real numbers. Then the relation

R = {(a, b) : 1 + a b > 0}

Q. Let R and S be two equivalence relations on set A. Prove that

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