Show that we can replace intervals of the form

(a, b] in the definition of the family of Borel sets by other classes of intervals, for instance, all closed intervals, all intervals [a, b),

a, b ∈ R, all intervals (a,∞), a ∈ R, all intervals [a,∞), a ∈ R, all intervals (−∞, b), b ∈ R, all intervals (−∞, b], b ∈ R.