Question

一个大型学区的所有高中都参加了卖 T 恤的募款活动。下面哪个选项在逻辑上等价于这句话：“没有比 Euclid HS 更大的学校卖出的 T 恤比 Euclid HS 更多”？

All the high schools in a large school district are involved in a fundraiser selling T-shirts. Which of the choices below is logically equivalent to the statement “No school bigger than Euclid HS sold more T-shirts than Euclid HS”?

所有比 Euclid HS 小的学校卖出的 T 恤都比 Euclid HS 少。

All schools smaller than Euclid HS sold fewer T-shirts than Euclid HS.

没有任何卖出 T 恤比 Euclid HS 更多的学校比 Euclid HS 更大。

No school that sold more T-shirts than Euclid HS is bigger than Euclid HS.

所有比 Euclid HS 大的学校卖出的 T 恤都比 Euclid HS 少。

All schools bigger than Euclid HS sold fewer T-shirts than Euclid HS.

所有卖出 T 恤比 Euclid HS 少的学校都比 Euclid HS 小。

All schools that sold fewer T-shirts than Euclid HS are smaller than Euclid HS.

所有比 Euclid HS 小的学校卖出的 T 恤都比 Euclid HS 多。

All schools smaller than Euclid HS sold more T-shirts than Euclid HS.

答案：B

知识点：逻辑推理

难度评级：900

解答：

原命题可写为：如果一所学校比 Euclid HS 更大，那么它卖出的 T 恤不比 Euclid HS 更多。

它的逆否命题是：如果一所学校卖出的 T 恤比 Euclid HS 更多，那么它不比 Euclid HS 更大。这正是选项 B 的表述，所以正确答案是 B。

The statement says: if a school is bigger than Euclid HS, then it did not sell more T-shirts than Euclid HS. Its contrapositive is: if a school sold more T-shirts than Euclid HS, then it is not bigger than Euclid HS. This is exactly choice B . Choice C is stronger than the original statement because it rules out a bigger school selling the same number of T-shirts.

Thus, the answer is B .

2022 AMC 10B 第 11 题

答案：B

难度评级：900

解答：

其他年份的第 11 题