Problem 5 - Entrance Test

Statements: 1. Some fruits are sweet. 2. All sweet things are healthy. Conclusions: I. Some fruits are healthy. II. All healthy things are fruits.

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: A

Let's represent the statements: Statement 1: Some fruits are sweet. (Overlap between Fruits and Sweet circles). Statement 2: All sweet things are healthy. (Sweet circle is entirely inside Healthy circle). Combining the statements: Since 'Some fruits are sweet' and 'All sweet things are healthy', it logically follows that the portion of fruits that are sweet must also be healthy. Therefore, 'Some fruits are healthy'. Now, let's analyze the conclusions: I. Some fruits are healthy. This conclusion directly follows from the combination of the two statements. Thus, Conclusion I follows. II. All healthy things are fruits. We only know that 'Some fruits are healthy'. It is possible for healthy things to exist that are not fruits (e.g., vegetables, exercise). So, Conclusion II does not necessarily follow. Therefore, only conclusion I follows.