Suppose that $(\mathbb Q,+)$ be the additive rational group and $H$ a subgroup of it. Which of the following statements is not true?
(a) If $\mathbb Q/H\cong \mathbb Q$, then $H=0$.
(b) If $H\neq 0$, then every proper subgroup of $\mathbb Q/H$ is of finite order.
(c) If $H\neq 0$, then every element of $\mathbb Q/H$ is of finite order.
(d) If $\mathbb Q/H$ is finite, then $H=\mathbb Q$.
I have tried to solve it. I am not able to draw conclusions. Please help me.