Prove either $I$ or $J$ is contained in $P$. Understanding the statement of the question.

Question

I am trying to prove this question:

Assume $R$ is commutative. Let $I$ and $J$ be ideals of $R$ and assume $P$ is a prime ideal of $R$ that contains $IJ$ (for example, if $P$ contains $I \cap J$). Prove either $I$ or $J$ is contained in $P$.

But I do not understand what is the relation of the prime ideal $P$ being containing $IJ$ and giving example of that by $P$ containing $I \cap J$ (what is the relation between the 2 ideals $IJ$ and $I \cap J$) could someone explain this to me please?

Answer 1

We always have $IJ \subset I\cap J$, so $I\cap J \subset P \implies IJ \subset P$.