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.

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.