0<k<n<k+2. Which of the following statements must be true?(Ⅰ) If n is an intege

游客2024-01-12  18

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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