A ball is a sphere. All spheres are round. Some round things are mesmerizing. Which of the following conclusions is NECESSARILY TRUE? Conclusions: I. All balls are mesmerizing. II. All round things are spheres. III. Some mesmerizing things are spheres.
Correct answer: A. III
- A. III
- B. I and II
- C. Il and III
- D. I and III
Explanation
I. "All balls are mesmerizing" is not necessarily true. The statements provided do not establish a direct connection between all balls and being mesmerizing. So, this conclusion cannot be necessarily true. II. "All round things are spheres" is not necessarily true either. While it is true that all spheres are round, the statements do not provide enough information to conclude that all round things are spheres. There can be other objects that are round but not spherical. III. "Some mesmerizing things are spheres" is necessarily true. The statements establish that "Some round things are mesmerizing," and since all spheres are round (as stated in the first premise), it is necessarily true that some mesmerizing things are spheres. So, the correct conclusion is III, making option A the correct choice.
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About Logical Deductions
Logical deductions require conclusions to be drawn from stated facts, conditions and relationships without adding outside information. The work includes handling all, some and none statements, necessary and sufficient conditions, ordering restrictions, true or false conclusions, and the difference between what must be true and what could be true.
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