1968 AMC 12 第 10 题

Question

假设对某所学校，下列陈述为真：

\mathrm{I}

：有些学生不诚实。

\mathrm{II}

：所有兄弟会成员都诚实。

必然可以得出的结论是：

Assume that, for a certain school, it is true that

\mathrm{I}:

Some students are not honest.

\mathrm{II}:

All fraternity members are honest.

A necessary conclusion is:

有些学生是兄弟会成员

Some students are fraternity members

有些兄弟会成员不是学生

Some fraternity members are not students

有些学生不是兄弟会成员

Some students are not fraternity members

没有兄弟会成员是学生

No fraternity member is a student

没有学生是兄弟会成员

No student is a fraternity member

选取陈述

\mathrm{I}

保证存在的那种学生

Choose a student whose existence is guaranteed by statement

\mathrm{I}

根据陈述

\mathrm{II}

，这名不诚实的学生可能是兄弟会成员吗？

Could that dishonest student be a fraternity member under statement

\mathrm{II}?

陈述

\mathrm{I}

保证存在一名不诚实的学生。陈述

\mathrm{II}

说明每位兄弟会成员都诚实，所以这名不诚实的学生不可能是兄弟会成员。因此，有些学生不是兄弟会成员。

因此，正确答案是 C。

Statement

\mathrm{I}

guarantees a dishonest student. Statement

\mathrm{II}

says every fraternity member is honest, so that dishonest student cannot be a fraternity member. Hence some student is not a fraternity member.

Therefore, the correct answer is C.

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