P3090
Bijectivity is clear from the definition. Further, we have
\begin{equation}
f^{-1} B
= f^{-1} \{ b \}
= \{ 1 \}
\subseteq \{ 0, 1 \}
= A
\end{equation}
and
\begin{equation}
f A
= f \{ 0, 1 \}
= \{ a, b \}
\supset \{ b \}
= B
\end{equation}
$\square$
