= Union and intersection of set families
{title2=$\mathcal A\vee\mathcal B,\quad\mathcal A\wedge\mathcal B$}
For <set families>, $\mathcal A\vee\mathcal B=\{A\cup B:A\in\mathcal A,B\in\mathcal B\}$ and $\mathcal A\wedge\mathcal B=\{A\cap B:A\in\mathcal A,B\in\mathcal B\}$. These are families of distinct sets, rather than multisets indexed by pairs. The <four functions theorem> gives $|\mathcal A\vee\mathcal B|\,|\mathcal A\wedge\mathcal B|\ge|\mathcal A|\,|\mathcal B|$. Complementing one input family yields the analogous product bound for pairwise <set differences>.
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