Assume that $P(A)=P(B) .$ Show that $A=B$.
Assume that $P(A)=P(B) .$ Show that $A=B$.
Let $P(A)=P(B)$
To show: $A=B$
Let $x \in A$
$A \in P(A)=P(B)$
$\therefore x \in C,$ for some $C \in P(B)$
Now, $C \subset B$
$\therefore x \in B$
$\therefore A \subset B$
Similarly, $B \subset A$
$\therefore A=B$
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