Let N⊆ℝ be non-Lebesgue-measurable. P:the irrational points of N form a measurable set. Q:the boundary of N has positive Lebesgue outer measure. Choose truth values.
Removing a countable set cannot turn a nonmeasurable set into a measurable one: otherwise adding back N∩ℚ would make N measurable. If the boundary had outer measure zero, N would differ from its open interior only by a subset of a null set, hence be measurable by completeness. Thus P false and Q true. **B**.
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