• Interaction With Differences. We have equalities of sets
    \begin{align*} \webleft [U\setminus V,W\webright ]_{X} & = \webleft [U,W\webright ]_{X}\cup \webleft [V^{\textsf{c}},W\webright ]_{X}\\ & = \webleft [U,W\webright ]_{X}\cup \webleft [U,V\webright ]_{X},\\ \webleft [U,V\setminus W\webright ]_{X} & = \webleft [U,V\webright ]_{X}\setminus \webleft (U\cap W\webright )\end{align*}

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


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