WeBWorK Standalone Renderer

Order 8 of the following sentences so that they form a logical proof of the statement:

$\mathcal{P}(B)\cup \mathcal{P}(D)\subseteq \mathcal{P}(B\cup D)$

Choose from these sentences:

$A$ is an element of $\mathcal{P}(B \cup D)$
$A$ is an element of $B \cup D$
$A$ is an element of $\mathcal{P}(B)$ or $A$ is an element of $\mathcal{P}(D).$
$\mathcal{P}(B)$ and $\mathcal{P}(D)$ are nonempty since all power sets contain at least the empty set.
$A$ is a subset of $B.$
Let $A$ be an element of $\mathcal{P}(B) \cup \mathcal{P}(D).$
Without loss of generality, assume $A$ is an element of $\mathcal{P}(B).$
Suppose $B$ and $D$ are sets.
$A$ is a subset of $B \cup D.$

Your Proof:

Choose from these sentences:

$A$ is an element of $\mathcal{P}(B \cup D)$
$A$ is an element of $B \cup D$
$A$ is an element of $\mathcal{P}(B)$ or $A$ is an element of $\mathcal{P}(D).$
$\mathcal{P}(B)$ and $\mathcal{P}(D)$ are nonempty since all power sets contain at least the empty set.
$A$ is a subset of $B.$
Let $A$ be an element of $\mathcal{P}(B) \cup \mathcal{P}(D).$
Without loss of generality, assume $A$ is an element of $\mathcal{P}(B).$
Suppose $B$ and $D$ are sets.
$A$ is a subset of $B \cup D.$

Your Proof: