If $\mathbb{P}$ be a poset, $\dot{Q}$ a $\mathbb{P}$-name and $\mu$ an infinite cardinal such that $\Vdash 0<|\dot{Q}|\leq\mu$.
$(a)$ Exist names $\langle \dot{q}_\alpha\rangle_{\alpha<\mu}$ such that $\Vdash \dot{Q}=\{\dot{q}_\alpha:\alpha< \mu \} $.
$(b)$ Exist an $\dot{Q'}$ such that |$\text{dom}(\dot{Q'})|\leq \mu$ and $\Vdash \dot{Q}=\dot{Q'}.$
I'm beginning to study forcing and I would like to solve this simple question.
I have problems in making it. A suggestion to solve it please.