Sum of two indicator functions: $\mathbb{1}_A - \mathbb{1}_B$

Question

Let $A,B \subset \mathbb{R}^d$. Let us recall that $\mathbb{1}_A$ is the indicator function of $A$ defined by: $\mathbb{1}_A(x)=1$ if $x \in A$ and equals to zero otherwise.

Now, I m looking for $\mathbb{1}_A-\mathbb{1}_B$, so computed the folllowing: $\mathbb{1}_A(x)-\mathbb{1}_B(x)=0$ is $x \in A \cap B$, equals to $1$ if $x \in A\backslash B$ (if $B \subset A$), equals to $-1$ if $x \in B\backslash A$ (if $A \subset B$).

Is there a better representation of $\mathbb{1}_A-\mathbb{1}_B$?