$15 \cdot 25$ In a certain school, assume
I : Some students are dishonest.
II : All club members are honest.
The necessary conclusion that can be drawn is
(A) Some students are club members.
(B) Some club members are not students.
(C) Some students are not club members.
(D) No club member is a student.
(E) No student is a club member.
(19th American High School Mathematics Examination, 1968)
[Solution] Conclusions $(A),(B)$ require the "set of club members" to be a non-empty set, while assumptions I, II do not require this;

Furthermore, if the "set of club members" is a non-empty subset of the "set of all students", then conclusions $(D),(E)$ do not hold.

Moreover, from I we know that there are dishonest students, and from II we know that these people are not club members, so (C) is true.
Therefore, the answer is $(C)$.