1. Let $A, B, C$ be three sets. Then “$B, C$ are both subsets of $A$” is a ( ) condition for “$(A \cap B) \cup (A \cap C) = B \cup C$” to hold.
(A) Sufficient but not necessary
(B) Necessary but not sufficient
(C) Sufficient and necessary
(D) Neither sufficient nor necessary
$-1 . C$.
If $B$ and $C$ are both subsets of $A$, then
$$
(A \cap B) \cup (A \cap C) = B \cup C \text{. }
$$

Conversely, if equation (1) holds, then since $A \cap B$ and $A \cap C$ are both subsets of $A$, it follows that $B \cup C$ is a subset of $A$, i.e., $B$ and $C$ are both subsets of $A$.