= Solution
{c}
A <Lebesgue null set> $E\subset\mathbb R$ can, for every $\epsilon>0$, be covered by countably many open intervals whose total length is less than $\epsilon$. Equivalently, its Lebesgue outer measure is zero.
If $E_j$ is null, choose for it such a cover of total length below $\epsilon 2^{-j}$, $j\geq1$. The union of these countably many countable covers covers $\bigcup_jE_j$ and has total length below $\epsilon$. Since $\epsilon$ is arbitrary, \b[a countable union of null sets is null].
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