Problem 17 - Entrance Test

Statements: 1. Some flowers are red. 2. Some red things are beautiful. Conclusions: I. Some flowers are beautiful. II. Some beautiful things are flowers.

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: Some flowers are red. (Overlap between Flowers and Red circles). Statement 2: Some red things are beautiful. (Overlap between Red and Beautiful circles). Now, let's analyze the conclusions: I. Some flowers are beautiful. We know 'Some flowers are red' and 'Some red things are beautiful'. However, there is no definite link established between 'flowers' and 'beautiful'. The red things that are flowers might not be the same red things that are beautiful. It's possible for some flowers to be beautiful, and it's also possible for no flowers to be beautiful. So, Conclusion I does not necessarily follow. II. Some beautiful things are flowers. 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. Since neither conclusion can be definitively inferred and they do not form an 'either/or' complementary pair (both are 'Some A are B' type statements), neither conclusion I nor II follows.