Syllogistic inference about carpeting and color: All offices on the 9th floor have wall-to-wall carpeting, and no wall-to-wall carpeting is pink; decide whether the conclusion "None of the 9th-floor offices has pink wall-to-wall carpeting" must follow.
Logical Reasoning
Logical Problems
Difficulty: Easy
Choose an option
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ADefinitely true
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BDefinitely false
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CCannot be determined from the given premises
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DTrue only if all carpets are the same color
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ETrue unless an office lacks carpeting
Answer
Correct Answer: Definitely true
Explanation
Given data
- Premise 1: All 9th-floor offices have wall-to-wall carpeting.
- Premise 2: No wall-to-wall carpeting is pink.
- Conclusion to test: No 9th-floor office has pink wall-to-wall carpeting.
Concept / ApproachUse categorical logic: If all items in Group A have Property C, and nothing with Property C can be pink, then nothing in Group A has pink carpeting.
Step-by-step reasoningStep 1: Every 9th-floor office ∈ {carpeted}.Step 2: {carpeted} ∩ {pink} = ∅ (by Premise 2, carpets cannot be pink).Step 3: Therefore, for any 9th-floor office, "pink wall-to-wall carpeting" is impossible.
Verification / Alternative viewContrapositive thinking: If an office had pink wall-to-wall carpeting, then there would exist pink wall-to-wall carpeting, contradicting Premise 2.
Common pitfalls
- Assuming some 9th-floor offices might lack carpets; Premise 1 rules that out.
Final AnswerDefinitely true.