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Consider the following relations: R = {(...

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 , pandqa r ei n t e g e r ss u c ht h a tn ,q"!="0andq m = p n"}` . Then (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation

A

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

B

neither R nor S is an equivalence relation

C

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

D

R and S both are equivalence relations.

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The correct Answer is:
C
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  • 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)) where m, n, p and q are integers such that n, q ne 0 and qm = pn}. Then

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