Consider the following relations:
R={(x, y) : x, y are real numbers and x = wy for some rational number w}
S = \(\left\{\frac{m}{n}, \frac{p}{q}: m, n, p, q \in Z\right.\) such that n, q ≠ 0 and qm = pn}
Then,
1
S is an equivalence relation but R is not an equivalence relation
2
R and S both are equivalence relations
3
R is an equivalence relation but S is not an equivalence relation
4
neither R nor S is an equivalence relation