2. 外语
  3. 0＜k＜n＜k+2. Which of the following statements must be true? (Ⅰ) If n is an integer, n cannot equal to k+1. (Ⅱ) If k is not an int

0＜k＜n＜k+2. Which of the following statements must be true? (Ⅰ) If n is an integer, n cannot equal to k+1. (Ⅱ) If k is not an int

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问题 0＜k＜n＜k+2. Which of the following statements must be true?
(Ⅰ) If n is an integer, n cannot equal to k+1.
(Ⅱ) If k is not an integer, there exists an integer n such that (k-n)(n-k-1)＞0.
(Ⅲ) If n is an integer, and k is not an integer, |k+1-n|＞|n-k-2|.
选项 A、(Ⅰ)(Ⅱ)
B、(Ⅱ) only
C、(Ⅱ)(Ⅲ)
D、(Ⅲ) only
E、none of the above
答案B
解析 根据题目，如果n是整数，k也是整数，那么n=k+1；如果k不是整数，那么n＞k+1或n＜k+1。
(Ⅰ)如果k是整数时，n=k+1，(Ⅰ)不正确。
(Ⅱ)如果k＜n＜k+1时，k-n＜0，当n＜k+1时，n-k-1＜0，使得(k-n)(n-k-1)＞0成立，(Ⅱ)正确。
(Ⅲ)|k+1-n|表示n到k+1的距离，|n-k-2|表示n到k+2的距离，若n＞k+1，则无法判断n到k+1和k+2的距离的长短，(Ⅲ)不正确。
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