Claim:A ∩ (B 1 ∪ ... ∪ B n) ⊆ (A ∩ B 1) ∪ ... ∪ (A ∩ B n)

From CS2800 wiki
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].