Statements: All pens are blue. No blue is black. Conclusions: I. No pen is black. II. Some pens are black. III. All blacks are pens.
Correct answer: B. Only I
- A. Only II
- B. Only I
- C. II and III
- D. None
Explanation
To solve this problem, we need to evaluate each conclusion based on the given statements:1. The statement 'All pens are blue' implies that the category of pens is fully contained within the category of blue things.2. The statement 'No blue is black' implies that there is no overlap between the categories of blue things and black things.Conclusion I ('No pen is black') logically follows because if all pens are blue and no blue is black, then pens cannot be black.Conclusion II ('Some pens are black') contradicts the statements because, as established, no pen can be black.Conclusion III ('All blacks are pens') is incorrect since the statement 'No blue is black' does not provide any information about the relationship between pens and black items beyond the fact that they cannot overlap due to the color restrictions.
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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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