Please answer the following question as much as possible, thank you!

Let Q be the set of rational numbers. Let B(R) = of{(-co, x] :x E R} ) be the Borel field. Assume P is a probability measure on B(R). Prove or disprove the following. (a) 5 points B(IR) = 0(1(-0o, q] : q E Q}).(b) 5 points B(R) = o({{q) : qEQ}).(c) 5 points If B1, B2, . ..E B(R) so that _f, P(B;) = co then P(lim infn +0% Bn) = 1/2