Question

离散数学 sufficient 和necessary的问题

For n belongs to N ,which of the following :
(i) 3/n
(ii) 9/n
(iii) 3/n^2
(iv) 12/n
(v) n even ^ 3/n

(a) Is (are) necessary for n to be divisible by 6? Briefly explain your answers.
(b) Is (are) sufficient for 6 j n? Briefly explain your answers.

Answer 1

不懂你的记号。
1）3/n 指的是 n 分之 3，或是 3 整除 n？后者应该是 3|n。
2） 6 j n 是啥意思？

追问

3除n
6 j n也是除的意思。pdf复制出的问题 大神求帮忙

追答

(a) Is (are) necessary for n to be divisible by 6? Briefly explain your answers.
(i) 3|n。
For 6|n ==> n=6k=3(2k) ==> 3|n。

(iii) 3|n^2。
For 6|n ==> n=6k=3(2k) ==> n^2=36k^2=3(12k^2) ==> 3|n。

(b) Is (are) sufficient for 6 j n? Briefly explain your answers.
(iv) 12|n。
For 12|n ==> n=12k=6(2k) ==> 6|n。

(v) n even ∧ 3|n。
For n=3k∧n even ==> n=3k∧2|k ==> n=3k∧k=2j ==> n=6j ==> 6|n。