Question

Carroll 老师承诺：即将到来的考试中，凡是把所有选择题都答对的人，都会在这次考试中得到 A。以下哪一句一定能由此在逻辑上推出？

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，那么他把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，那么他把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：1100

解答：

这个承诺是“全部答对 $\Rightarrow$ 得到 A”。一个蕴含命题只与它的逆否命题等价： “没有得到 A $\Rightarrow$ 没有全部答对”。

“没有全部答对”表示至少有一道题答错，这正是选项 B。逆命题和否命题都不能推出，而“全部答错” 比这个否定强得多。

所以正确答案是 B。

The promise is "all right $\Rightarrow$ A." An implication is equivalent only to its contrapositive: "not A $\Rightarrow$ not all right."

"Not all right" means at least one question was wrong, which is exactly statement B. The converse and inverse do not follow, and getting "all wrong" is a much stronger claim than the negation.

Thus, the correct answer is B.

2017 AMC 12A 第 3 题

答案：B

难度评级：1100

解答：

其他年份的第 3 题