Which of these statements about the floor and ceiling functions are correct?
Statement I: ⌊2x⌋ = ⌊x⌋ + ⌊x + (1/2)⌋ for all real number x.
Statement II: ⌈x + y⌉ = ⌈x⌉ + ⌈y⌉ for all real numbers x and y.