Question

Carroll 老师承诺：即将到来的考试中，所有选择题都答对的人都会得到 A。下面哪一个陈述在逻辑上必然成立？

Ms. Carroll promised that anyone who got all the multiple choice questions right on the upcoming exam would receive an A on the exam. Which one of these statements necessarily follows logically?

如果 Lewis 没有得到 A，那么他所有选择题都答错了。

If Lewis did not receive an A, then he got all of the multiple choice questions wrong.

如果 Lewis 没有得到 A，那么他至少答错了一道选择题。

If Lewis did not receive an A, then he got at least one of the multiple choice questions wrong.

如果 Lewis 至少答错了一道选择题，那么他没有得到 A。

If Lewis got at least one of the multiple choice questions wrong, then he did not receive an A.

如果 Lewis 得到了 A，那么他所有选择题都答对了。

If Lewis received an A, then he got all of the multiple choice questions right.

如果 Lewis 得到了 A，那么他至少答对了一道选择题。

If Lewis received an A, then he got at least one of the multiple choice questions right.

答案：B

知识点：逻辑推理

难度评级：900

小提示：

把老师的承诺翻译成一个蕴含命题。

Translate the promise as an implication

大提示：

使用这个命题的逆否命题。

Use the contrapositive of the statement

解答：

这个承诺是说：只要所有选择题都答对，就一定能得到 A。它的逆否命题是：任何没有得到 A 的人，一定没有把所有选择题都答对。换句话说，那个人至少答错了一道选择题。

所以正确答案是 B。

The promise says that getting every multiple choice question right guarantees an A. Its contrapositive is that anyone who did not receive an A must not have gotten every multiple choice question right. In other words, that person got at least one multiple choice question wrong.

Thus, B is the correct answer.

2017 AMC 10A 第 6 题

答案：B

难度评级：900

小提示：

大提示：

解答：

其他年份的第 6 题