• Interaction With Symmetric Differences. We have
    \[ \chi _{U\mathbin {\triangle }V}=\chi _{U}+\chi _{V}-2\chi _{U\cap V} \]

    and thus, in particular, we have

    \[ \chi _{U\mathbin {\triangle }V}\equiv \chi _{U}+\chi _{V}\ \ (\mathrm{mod}\ 2) \]

    for each $U,V\in \mathcal{P}\webleft (X\webright )$.


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