Statements: Some shirts are pants. All pants are cotton. Conclusions: I. Some shirts are cotton. II. All cottons are shirts. III. Some pants are shirts.
Correct answer: A. I and III
- A. I and III
- B. Only III
- C. Only II
- D. None
Explanation
To solve this, visualize the relationships using Venn diagrams. The statement 'Some shirts are pants' means there's an overlap between shirts and pants. The statement 'All pants are cotton' means the circle representing pants is completely within the circle for cotton. Thus, some shirts, which are pants, are also within the cotton circle, making Conclusion I true. Conclusion II is incorrect because not all cottons are shirts; the premise only establishes that all pants (not all cotton) are inside the cotton circle. Conclusion III is correct because the premise explicitly states 'Some shirts are pants.' Therefore, the correct answer is Option A: 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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