Problem 19 - Entrance Test

Statements: 1. All books are papers. 2. No paper is a pen. Conclusions: I. No book is a pen. II. Some papers are books.

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: E

Let's represent the statements: Statement 1: All books are papers. (Books circle is entirely inside Papers circle). Statement 2: No paper is a pen. (Papers circle and Pens circle are separate). Now, let's analyze the conclusions: I. No book is a pen. Since 'All books are papers' and 'No paper is a pen', it means that if books are inside papers, and papers are separate from pens, then books must also be separate from pens. Thus, Conclusion I follows directly. II. Some papers are books. If 'All books are papers', it means that all the members of the 'Books' set are also members of the 'Papers' set. Therefore, 'Some papers are books' (specifically, the papers that are books) is a valid conclusion. Thus, Conclusion II follows. Therefore, both conclusions I and II follow.