Problem 15 - Entrance Test

Statements: 1. All teachers are educated. 2. All educated persons are employed. Conclusions: I. All teachers are employed. II. Some employed persons are teachers.

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 teachers are educated. (Teachers circle is entirely inside Educated circle). Statement 2: All educated persons are employed. (Educated circle is entirely inside Employed circle). Combining the statements: Since 'All teachers are educated' and 'All educated persons are employed', it logically follows that 'All teachers are employed'. Now, let's analyze the conclusions: I. All teachers are employed. This conclusion directly follows from the combination of the two statements. Thus, Conclusion I follows. II. Some employed persons are teachers. If 'All A are B' is true, then 'Some B are A' is also true. Since 'All teachers are employed' is true, it means that the set of teachers is a subset of employed persons. Therefore, 'Some employed persons are teachers' is also true. Thus, Conclusion II follows. Therefore, both conclusions I and II follow.