Statements: Some players are athletes. All athletes are winners. Conclusions: I. Some players are winners. II. All players are winners. III. Some winners are players.
Correct answer: C. I and III
- A. Only I
- B. Only III
- C. I and III
- D. All follow
Explanation
To solve this, analyze the logical flow: The statement 'Some players are athletes' means there's an overlap between players and athletes. The statement 'All athletes are winners' means the category of athletes is entirely within the category of winners. Therefore, we can deduce that some players, who are athletes, are winners (Conclusion I), and some winners are players (Conclusion III). However, Conclusion II, 'All players are winners', is incorrect because the statement only confirms that some players are athletes, not all. Thus, the correct answer is Option C: I and III.
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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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