Problem 3 - Entrance Test

Statements: 1. No student is a teacher. 2. All teachers are intelligent. Conclusions: I. No student is intelligent. II. Some intelligent are not students.

A. A. Only conclusion I follows.B. B. Only conclusion II follows.C. C. Either conclusion I or II follows.D. D. Neither conclusion I nor II follows.E. E. Both conclusions I and II follow.

Correct: B

Let's represent the statements: Statement 1: No student is a teacher. (Students circle and Teachers circle are separate). Statement 2: All teachers are intelligent. (Teachers circle is entirely inside Intelligent circle). Now, let's analyze the conclusions: I. No student is intelligent. From the statements, we know that students are not teachers, and teachers are intelligent. However, this does not mean that students cannot be intelligent. There could be intelligent people who are not teachers but are students. So, Conclusion I does not necessarily follow. II. Some intelligent are not students. Since 'All teachers are intelligent' (Statement 2) and 'No student is a teacher' (Statement 1), it implies that the group of 'teachers' (who are also 'intelligent') cannot be 'students'. Therefore, 'Some intelligent (specifically, the teachers who are intelligent) are not students' is a valid conclusion. Thus, Conclusion II follows. Therefore, only conclusion II follows.