Chapter 2, Problem 2.5TE

For any sequence of events $E_1,E_2,\mathrm{...},$ define a new sequence $F_1,F_2,\mathrm{...}$ of disjoint events (that is. events such that $F_i{F}_j=\varphi$ whenever $i\ne j$ ) such that for all $n\ge 1$, ${\displaystyle \underset{1}{\overset{n}{\cup }}{F}_i}={\displaystyle \underset{1}{\overset{n}{\cup }}{E}_i}$