Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; S = {(mn, pq) : m, n, p and q are integers such that n, q ≠ 0 and qm = pn}. Then which of the following is true?

xRy need not imply yRx. S: Since qm = pn, mn ~ mn (reflexive). mn ~ pq implies qm = pn; pq ~ mn implies pn = qm. Thus mn ~ pq implies pq ~ mn (symmetric). mn ~ pq, pq ~ rs implies qm = pn, ps = rq. Then qmps = pnrs, and qm/n = p/q = r/s = k, some rational number. Thus, qm = pn = k, ps = rq = k. Then qs = pn/m = rq/p. Hence, ms = rntransitive. S is an equivalence relation.