Mathematics · Calculus

Let f : [0, 3] → ℝ be defined by f(x) = min { x - ⌊x⌋, 1 + ⌊x⌋ - x } where ⌊x⌋ is the greatest integer less than or equal to x. Let P denote the set containing all x ∈ [0, 3] where f is discontinuous, and Q denote the set containing all x ∈ (0, 3) where f is not differentiable. Then the sum of the number of elements in P and Q is equal to: