Let K be a nonempty subset of R^n, where n > 1. Which of the following statements must be true?
I. If K is compact, then every continuous real-valued function defined on K is bounded.
II. If every continuous real-valued function defined on K is bounded, then K is compact.
III. If K is compact, then K is connected.
(A)I only (B)II only (C)III only (D)I and II only
D