ThmDex – An index of mathematical definitions, results, and conjectures.
F10560
Formulation 0
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}
Then
(1) $f$ is a D468: Bijective map
(2) \begin{equation} f(A) \subseteq B \end{equation}
(3) \begin{equation} f^{-1}(B) \not\subseteq A \end{equation}