Problem 9 - Entrance Test

Statements: 1. All laptops are computers. 2. Some computers are expensive. Conclusions: I. Some laptops are expensive. II. Some expensive things are laptops.

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: D

Let's represent the statements: Statement 1: All laptops are computers. (Laptops circle is entirely inside Computers circle). Statement 2: Some computers are expensive. (Expensive circle overlaps with a portion of the Computers circle). Now, let's analyze the conclusions: I. Some laptops are expensive. Laptops are inside Computers. Expensive things overlap with Computers. However, the overlap of Expensive things and Computers might or might not include the Laptops part of Computers. There's no definite link to conclude 'Some laptops are expensive'. So, Conclusion I does not necessarily follow. II. Some expensive things are laptops. This is a conversion of Conclusion I. Since Conclusion I is not necessarily true, its conversion is also not necessarily true. So, Conclusion II does not necessarily follow. Therefore, neither conclusion I nor II follows.