Counterexample to disprove that $P(A-B) = P(A) - P(B)$?

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Assuming $P(A)$ is the power set of $A$, would this be a correct counterexample for the statement that $P(A-B) = P(A) - P(B)$?


Let $A = \{2, 3\}$ and $B = \{2\}$, therefore $C = \{3\}$.

$P(A-B) = P(C) = \{\{3\}, \{\varnothing\}\}$

\begin{align*} P(A) - P(B) &= \{\{2, 3\}, \{2\}, \{3\}, \{\varnothing\}\} - \{\{2\}, \{\varnothing\}\} \\ &= \{\{2, 3\}, \{3\}\} \end{align*}

As shown, $P(A-B)$ contains the empty set while $P(A) - P(B)$ does not and as such:

$$P(A-B) \ne P(A) - P(B)$$

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Comments from Cameron Williams and Asaf Karagila were incorporated in this answer.

Yes that would work.

In fact, $P(A) - P(B)$ never contains the empty set (as $\varnothing \in P(B)$), so any $A$ and $B$ suffice (even $A = B = \varnothing$).