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Consider the following relations : <br> $R = \{ (x, y) | x, \; y$ are real number and $x = wy$ for some rational number $w \}$; <br> $S = \{ (\frac{m}{n}, \frac{p}{q} ) | m, \; n, \; p $ and $q$ are integers such that $n, \;q \neq 0$ and $qm = pn \}$. Then

( A ) neither $R$ nor $S$ is an equivalence relation
( B ) $S$ is an equivalence relation but $R$ is not an equivalece relation
( C ) $R$ is an equivalence relation but $S$ is not an equivalence relation
( D ) $R$ and $S$ both are equivalence relations

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