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If <math>A</math> and <math>B</math> are two subsets of <math>X,</math> then
<math display=block>\begin{align}
\mathbf{1}_{A\cap B} &= \min\{\mathbf{1}_A,\mathbf{1}_B\} = \mathbf{1}_A \cdot\mathbf{1}_B, \\
\mathbf{1}_{A\cup B} &= \max\{{\mathbf{1}_A,\mathbf{1}_B}\} = \mathbf{1}_A + \mathbf{1}_B - \mathbf{1}_A \cdot\mathbf{1}_B,
\end{align}</math>
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