Problem 20 - Entrance Test

Statements: 1. Some squares are rectangles. 2. No rectangle is a circle. Conclusions: I. Some squares are not circles. II. All squares are circles.

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 squares are rectangles. (Overlap between Squares and Rectangles circles). Statement 2: No rectangle is a circle. (Rectangles circle and Circles circle are separate). Now, let's analyze the conclusions: I. Some squares are not circles. From Statement 1, there is a portion of squares that are rectangles. From Statement 2, no rectangle is a circle. Therefore, that specific portion of squares (which are rectangles) cannot be circles. This implies 'Some squares are not circles'. Thus, Conclusion I follows. II. All squares are circles. We know 'Some squares are rectangles' and 'No rectangle is a circle'. This implies that at least some squares are not circles. Therefore, 'All squares are circles' cannot be true. So, Conclusion II does not necessarily follow. Therefore, only conclusion I follows.