# Question about prime ideals and union of ideals

The questions asks to show that if $A$ is a ring and $I, J_{1}, J_{2}$ ideals of $A$, and $P$ is a prime ideal, then $I \subset J_{1} \cup J_{2} \cup P$ implies $I \subset J_{1}$ or $J_{2}$ or $P$.

I've been trying to work with the contrapositive and use that $I \subset J_{1} \cup J_{2}$ implies $I \subset J_{1}$ or $I \subset J_{2}$ in order to ascertain an element of $I$ that's not in the union, but I had no luck. Can anyone please shed some light? Thanks a lot in advance!

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Prime avoidance – Georges Elencwajg Sep 20 '12 at 17:21