Problem 6 - Entrance Test

Statements: 1. Some shirts are pants. 2. No pants are socks. Conclusions: I. Some shirts are not socks. II. No shirts are socks.

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 shirts are pants. (Overlap between Shirts and Pants circles). Statement 2: No pants are socks. (Pants circle and Socks circle are separate). Now, let's analyze the conclusions: I. Some shirts are not socks. From Statement 1, there is a portion of shirts that are pants. From Statement 2, no pants are socks. Therefore, that specific portion of shirts (which are pants) cannot be socks. This implies 'Some shirts are not socks'. Thus, Conclusion I follows. II. No shirts are socks. While the part of shirts that are pants are not socks, there might be other shirts (not pants) that could potentially be socks. The statements do not provide enough information to conclude that absolutely no shirts are socks. So, Conclusion II does not necessarily follow. Therefore, only conclusion I follows.