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JEE Main2010MathematicsSets and RelationsActual

Consider the following relations: R= (x, y) x, y are real numbers and x= wy for some rational number w ; S= ( m n , p q ) m, n, p . and q are integers such that n, q 0 and .q m=p n . Then

Options

  1. Aneither R nor S is an equivalence relation
  2. BS is an equivalence relation but R is not an equivalence relation
  3. CR and S both are equivalence relations
  4. DR is an equivalence relation but S is not an equivalence relation

Correct answer

D. R is an equivalence relation but S is not an equivalence relation

Step-by-step solution

xRy need not implies y R x S : m n s p q qm = pn m n s m n reflexive array ll m n s p q & p q s m n symmetric m n s p q , p q s r s & q m=p n, p s=r q m s=r n transitive. array S is an equivalence relation.

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