Statements: Some metals are hard. All hard things are useful. Conclusions: I. Some metals are useful. II. All metals are useful.
Correct answer: A. Only I
- A. Only I
- B. Only II
- C. Both
- D. None
Explanation
The correct answer is Option A: Only I. The first statement tells us that some metals are hard, and the second statement confirms that all hard things are useful. Therefore, it logically follows that some metals are useful, making Conclusion I true. Conclusion II is incorrect because the statements do not support the assertion that all metals are useful; they only establish that some metals are hard and thus some are useful. Option C is incorrect because it wrongly assumes both conclusions are valid, while Option D is incorrect because Conclusion I is valid.
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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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