MathDB

Set: one is contained in the union of other two

Source:

May 17, 2012

setset theoryintervalunionIntersection

Problem Statement

Let

I_1, I_2, I_3

be three open intervals of

\mathbb{R}

such that none is contained in another. If

I_1\cap I_2 \cap I_3

is non-empty, then show that at least one of these intervals is contained in the union of the other two.