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.

Correct — C. The three statements form a chain: some pineapples are oranges, all oranges are bananas, all bananas are plums.

Rule: a chain of universals carries a particular all the way through it. If some P are O, and every O ends up inside plums, then those P are plums too.

I. Some pineapples are plums. The pineapples that are oranges are bananas, and all bananas are plums. Follows.

II. All oranges are plums. Every orange is a banana and every banana is a plum. Follows.

III. No pineapple is a banana. The same chain puts some pineapples inside bananas, so this is contradicted, not merely unproven. Does not follow.

I and II follow and III does not — option (c).

Why the others are wrong

• (a)
  Only conclusions I and III follow — Conclusion III is contradicted by the statements, not just left unsupported: statement 1 puts some pineapples inside oranges and statement 2 puts every orange inside bananas.
• (b)
  Only conclusions II and III follow — Option (b) drops conclusion I, which the chain proves — the pineapples that are oranges end up inside plums. It also keeps III, which the statements rule out.
• (d)
  Only conclusion III follows — Option (d) accepts the conclusion the statements contradict and rejects the two they prove. Nothing in the three statements separates pineapples from bananas.

Two things decide a syllogism set like this one. First, a particular premise ('some pineapples are oranges') survives any number of universal premises stacked after it, so 'some pineapples are plums' is safe.

Second, a negative conclusion has a higher bar than a positive one. 'No pineapple is a banana' is not merely unproven here — the premises actively put some pineapples inside bananas, so it is false on the statements as given.

Key facts

• 'Some A are B' is symmetric: it also means some B are A.
• 'All A are B' together with 'All B are C' gives 'All A are C'.
• A 'No X is Y' conclusion fails the moment a premise places any X inside Y.

Common traps

• Rejecting the chain because oranges are not really bananas, which the instruction forbids.
• Marking conclusion I unproven because no single statement names pineapples and plums together.
• Reading conclusion III as unsupported when the statements actually contradict it.

No directly related past PYQ was found.