Three Points on a Line

Difficulty: Medium · Topics: Discrete Mathematics, Sets, Intervals

Three real numbers are marked on a number line in the order a, b, c from left to right, so a<b<c. The sets of the real numbers smaller than a, smaller than b and smaller than c are A, B and C respectively.

Which of the following statements are always true?

I. a∈(B-A)

II. b∈(A'cap C')

III. [a,b)subset(A'-B')