Question

Let Q be the set of rational numbers in (0,1) and ε > 0.

(a) Describe an open set V containing Q, such that m(V \Q) < ε.

(b) Describe a closed set F, F ⊂ I, I := (0,1)\Q, such that m(I \F) < ε.

where m(·) is the Lebesgue measure.