Charlie:

\[ f^{\ast}(P \vee Q) = \\{ \\{11 \\} \\} \]

makes no sense, because \\( \\{ \\{11 \\} \\} \\) is not even a partition of our set \\( \\{11, 22 \\} \\).

But there are tons of typos around here, which make this section very confusing. For example, \\(f\\) should be \\(i\\), and that's not all! Let me figure out what I meant to say, and fix it!