Please help me with a solution to this problem.
Let $R$ be a commutative ring. Let $A_1, A_2$ be two ideals of $R$, and $P_1, P_2$ two prime ideals of $R$.
Assume that $A_1 \cap A_2 \subseteq P_1 \cap P_2$. Show that there exist $i, j \in \{1,2\}$ such that $A_i \subseteq P_j$.