Question

Consider the following relations:
R = {(x, y) | x, y are real numbers and x = wy for some rational number w};
S {$\bigg \lgroup\frac{m}{n},\frac{p}{q}\bigg \rgroup$| m,n, p and q are integers such that n, q ≠ 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 equivalence relation
(c) R and S both are equivalence relations
(d) R is an equivalence relation but S is not an equivalence relation

Answer 1

(d) R is an equivalence relation but S is not an equivalence relation