Problem 11 - Entrance Test

Statements: 1. No house is an apartment. 2. All apartments are buildings. Conclusions: I. No house is a building. II. Some buildings are not houses.

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 house is an apartment. (Houses circle and Apartments circle are separate). Statement 2: All apartments are buildings. (Apartments circle is entirely inside Buildings circle). Now, let's analyze the conclusions: I. No house is a building. We know 'No house is an apartment' and 'All apartments are buildings'. This means the part of buildings that are apartments are not houses. However, there could be other buildings (not apartments) that could be houses. So, Conclusion I does not necessarily follow. II. Some buildings are not houses. Since 'All apartments are buildings' (Statement 2) and 'No house is an apartment' (Statement 1), it implies that the group of 'apartments' (which are also 'buildings') cannot be 'houses'. Therefore, 'Some buildings (specifically, the apartments that are buildings) are not houses' is a valid conclusion. Thus, Conclusion II follows. Therefore, only conclusion II follows.