  We show that assuming $\mathsf{ZF}+\mathsf{AD}^+ +$ "$V = \mathrm{L}
\bigl(\wp (\mathbb{R})\bigr)$", any poset which increases $\Theta$ does not
preserve the truth of $\mathsf{AD}$. We also show that in $\mathsf{ZF} +
\mathsf{AD}$, any non-trivial poset on $\mathbb{R}$ does not preserve the truth
of $\mathsf{AD}$. This answers the question of Chan and Jackson. Furthermore,
we show that under the assumptions $\mathsf{ZF}+\mathsf{AD}^+ +$ "$V =
\mathrm{L} \bigl(\wp (\mathbb{R})\bigr)$" + "$\Theta \text{ is regular}$",
there is a poset on $\Theta$ which adds a new subset of $\Theta$ while
preserving the truth of $\mathsf{AD}$. This answers the question of Cunningham.
