A subset $W$ of the set of real numbers is called a ring if it contains 1 and if for all $a, b \in W$, the numbers $a - b$ and $ab$ are also in $W$. Let $S = \left\{ \left. \frac{m}{2^n} \right\rvert\, m, n \text{ integers} \right\}$ and $T = \left\{ \left. \frac{p}{q} \right\rvert\, p, q \text{ integers}, q \text{ odd} \right\}$. Then\\
(A) neither $S$ nor $T$ is a ring\\
(B) $S$ is a ring, $T$ is not a ring\\
(C) $T$ is a ring, $S$ is not a ring\\
(D) both $S$ and $T$ are rings