Problem 14 - Entrance Test

Statements: 1. Some metals are hard. 2. Some hard substances are shiny. Conclusions: I. Some metals are shiny. II. No metal is shiny.

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: C

Let's represent the statements: Statement 1: Some metals are hard. (Overlap between Metals and Hard circles). Statement 2: Some hard substances are shiny. (Overlap between Hard and Shiny circles). Now, let's analyze the conclusions: I. Some metals are shiny. We know 'Some metals are hard' and 'Some hard substances are shiny'. However, there is no definite link established between 'metals' and 'shiny'. The hard substances that are metals might not be the same hard substances that are shiny. It's possible for some metals to be shiny, and it's also possible for no metals to be shiny. So, Conclusion I is not necessarily true (uncertain). II. No metal is shiny. Similarly, it's possible that no metals are shiny, but it's not certain. So, Conclusion II is also not necessarily true (uncertain). However, conclusions I (Some metals are shiny) and II (No metal is shiny) form a complementary pair (contradictory pair 'I' type and 'E' type propositions). If 'Some A are B' is false, then 'No A are B' must be true, and vice-versa. Since both are individually uncertain, one of them must be true. Therefore, 'Either conclusion I or II follows'.