Statements: Some pens are pencils. All pencils are erasers. Conclusions: I. Some pens are erasers. II. All pens are erasers. III. Some erasers are pens
Correct answer: A. Only I and III
- A. Only I and III
- B. Only II
- C. Only III
- D. Only I
Explanation
To solve this question, consider the logical deductions: Start with the statements 'Some pens are pencils' and 'All pencils are erasers'. From these, we can deduce: Conclusion I: 'Some pens are erasers' is valid because the pens that are pencils are also erasers.Conclusion II: 'All pens are erasers' is not valid because we have no information that all pens are pencils.Conclusion III: 'Some erasers are pens' is valid because the erasers that are pencils are also pens. Therefore, the correct conclusions are 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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