第 11 类 RD Sharma 解决方案 – 第 31 章导数 – 练习 31.4

问题 1. 写出下列每个陈述的否定：

(i) 对于每个 x ∈ N，x + 3 > 10

(ii) 存在 x ∈ N, x + 3 = 10

解决方案：

(i) The negation of the statement is “There exist x ∈ N, such that x + 3 <= 10.”

(ii) The negation of the statement is “There exist x ∈ N, such that x + 3 ≠ 10.”

问题 2. 否定以下每个陈述：

(i) 所有学生完成作业。

(ii) 存在一个等于其平方的数。

解决方案：

(i) Some of the students did not complete their homework.

(ii) For all real numbers x, x²≠x.”