Problem: For each real number , let be the largest integer not exceeding (i.e., the integer such that ). Which of the following statements is (are) true?
I. for all
II. for all and
III. for all and
Answer Choices:
A.
B. I only
C. I and II only
D. III only
E.
Solution:
If , then . Choosing shows that II and III are false.