Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: Some pineapples are oranges. All oranges are bananas. All bananas are plums. Conclusions: I. Some pineapples are plums. II. All oranges are plums. III. No pineapple is a banana.

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Step 1: Analyze the statements: - Some pineapples are oranges. - All oranges are bananas. - All bananas are plums. Step 2: From 'All oranges are bananas' and 'All bananas are plums', we can conclude 'All oranges are plums' (Conclusion II). Step 3: Since some pineapples are oranges and all oranges are plums, those pineapples that are oranges are also plums. Hence, 'Some pineapples are plums' (Conclusion I) follows. Step 4: Conclusion III states 'No pineapple is a banana'. However, since some pineapples are oranges and all oranges are bananas, it is possible that some pineapples are bananas. Therefore, Conclusion III does not follow. Final conclusion: Only conclusions I and II follow.

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