$\Vdash_{\mathbb{P}} \check{\mathbb{Q}}$ is not countably closed. Where $\mathbb{P} = Add(\omega, 1)$, $\mathbb{Q} = Add(\omega_1, 1)$
I would like to prove this. But I'm sort of lost- I might be drastically overthinking it. Most I can say is that the offending sequence that witnesses failure of countable closure will probably come from the new subset of $\omega$ being added, but that doesn't help too much. I have tried some things related to Easton's theorem but I think I may be off target there. Would appreciate some help.