For any [math]n ≥ 2
[/math],
[math]A \href{/cs2800/wiki/index.php/%E2%88%A9}{∩} (B_1 \href{/cs2800/wiki/index.php/%E2%88%AA}{∪} \cdots \href{/cs2800/wiki/index.php/%E2%88%AA}{∪} B_n) \href{/cs2800/wiki/index.php/%E2%8A%86}{⊆} (A \href{/cs2800/wiki/index.php/%E2%88%A9}{∩} B_1) \href{/cs2800/wiki/index.php/%E2%88%AA}{∪} \cdots \href{/cs2800/wiki/index.php/%E2%88%AA}{∪} (A \href{/cs2800/wiki/index.php/%E2%88%A9}{∩} B_n)
[/math]
Note: this claim is also obviously true for [math]n = 1
[/math], and
if you take the convention that the union of an empty collection of sets
is ∅, then it is also true for [math]n=0
[/math].
