Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: Some boxes are cartons. All cartons are papers. Some cartons are utensils. Conclusion (I): No box is a utensil. Conclusion (II): Some papers are utensils.

Correct — A. Only conclusion (II) follows, which is option (a).

Rule: a conclusion follows only if it holds in every arrangement the statements allow, not in one convenient diagram.

Conclusion (II) is forced. Some cartons are utensils, and all cartons are papers, so those carton-utensils are papers as well. Some papers are utensils.

Conclusion (I) is not. Some boxes are cartons and some cartons are utensils, so one object could be box, carton and utensil at once. No box is a utensil is merely possible.

Why the others are wrong

• (b)
  Only conclusion (I) follows — This has the two the wrong way round. (I) is only a possibility — nothing separates boxes from utensils — while (II) is forced by the carton-to-paper chain.
• (c)
  Both conclusions (I) and (II) follow — It accepts (I). But the statements permit an overlap in which some boxes are cartons that are utensils, so a flat No box is a utensil cannot be asserted.
• (d)
  Neither conclusion (I) nor (II) follows — It ignores the chain. All cartons are papers, so the cartons that happen to be utensils are papers too, and that makes (II) certain.

A syllogism asks what must be true, not what could be true.

'Some X are Y' says only that the two sets overlap somewhere. It never fixes the size of the overlap, and it never denies a further overlap elsewhere.

So a negative conclusion like 'No box is a utensil' can be drawn only when the statements actively push the two sets apart. Nothing here does.

The positive chain behaves differently. 'Some cartons are utensils' plus 'All cartons are papers' carries those utensils into papers, and that transfer is unavoidable.

Key facts

• A conclusion follows only if it is true in every arrangement the statements allow.
• Some A are B combined with All B are C always yields Some A are C.
• Two 'some' statements sharing a middle term never force a negative conclusion.

Common traps

• Reading 'Some cartons are utensils' as if it also said some cartons are not utensils.
• Accepting a negative conclusion because no statement links boxes to utensils — an absent link is not a denial.

No directly related past PYQ was found.