Are these sets Borel-measurable? Are the following sets Borel-measurable and if so, what is the value of the measure? 
1) A = {(x,y) ∈ $[0,1]^2$| x and y rational}
2) B = {(x,y) ∈ $[0,1]^2$ | x or y rational}
3) C = {(x,y) ∈ $[0,1]^2$ | x and y irrational}
4) D = {(x,y) ∈ $[0,1]^2$ | x=y}

All given sets are Borel-measurable and therefore the Borel-measure coincides with the Lebesgue-measure.
