• Interaction With Unions III. We have equalities of sets
    \begin{align*} U\setminus \webleft (V\cup W\webright ) & = \webleft (U\cup W\webright )\setminus \webleft (V\cup W\webright )\\ & = \webleft (U\setminus V\webright )\setminus W\\ & = \webleft (U\setminus W\webright )\setminus V \end{align*}

    for each $X\in \text{Obj}\webleft (\mathsf{Sets}\webright )$ and each $U,V,W\in \mathcal{P}\webleft (X\webright )$.


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