Let $f : \{ 0, 1 \} \to \{ a, b \}$ be a
D18: Map such that
| (i) |
\begin{equation}
f(0)
= a
\end{equation}
|
| (ii) |
\begin{equation}
f(1)
= b
\end{equation}
|
| (iii) |
\begin{equation}
A : = \{ 0 \}
\end{equation}
|
| (iv) |
\begin{equation}
B : = \{ a, b \}
\end{equation}
|
Bijectivity is clear from the definition. Further, we have
\begin{equation}
f A
= f \{ 0 \}
= \{ a \}
\subseteq \{ a, b \}
= B
\end{equation}
and
\begin{equation}
f^{-1} B
= f^{-1} \{ a, b \}
= \{ 0, 1 \}
\supset \{ 0 \}
= A
\end{equation}
$\square$
