If I have a set $A = \{1, 3\}$ and a set $B = \{2, 4\}$ where $P(A) = \{∅, \{1\}, \{3\}, \{1, 3\}\}$ and $P(A) = \{∅, \{2\}, \{4\}, \{2, 4\}\}$
if I do $P(A) - P(B)$, do I get a set like $\{\{1\}, \{3\}, \{1, 3\}\}$?
This is the original problem, it is the 5.b. I'm doing practice because I have a test
Your solution is correct. The empty set that is an element of $\mathcal P(A)$ is the same as the empty set that is the element of $\mathcal P(B)$, so removing all elements of $\mathcal P(B)$ eliminates it from $\mathcal P(A)$ and leaves the rest because there are no other elements shared.