Statement I: ⌊2x⌋ = ⌊x⌋ + ⌊x + 1/2⌋ for every real x. Statement II: ⌈x + y⌉ = ⌈x⌉ + ⌈y⌉ for all real x and y.

1. ABoth Statement I and Statement II are true
2. BBoth Statement I and Statement II are false
3. CStatement I is true but Statement II is false
4. DStatement I is false but Statement II is true 5

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: C. Statement I is true but Statement II is false

Explanation

Statement I is Hermite's identity (true). Statement II fails for x = y = 0.5: ⌈1⌉ = 1 but ⌈0.5⌉ + ⌈0.5⌉ = 2.