Let $X$ be a D11: Set.
The indicator function on $X$ with respect to $E \subseteq X$ is the D992: Function \begin{equation} X \to \{ 0, 1 \}, \quad x \mapsto \begin{cases} 1, \quad & x \in E \\ 0, \quad & x \in X \setminus E \end{cases} \end{equation}

Let $X$ be a D11: Set such that

(i)	$E \subseteq X$ is a D78: Subset of $X$

The indicator function on $X$ with respect to $E$ is the D218: Boolean function \begin{equation} X \to \{ 0, 1 \}, \quad x \mapsto |E \cap \{ x \}| \end{equation}