Statements: All the papers are books. All the bags are books. Some purses are…
2025
Statements: All the papers are books. All the bags are books. Some purses are bags.
Conclusions:
I. Some papers are bags.
II. Some books are papers.
III. Some books are purses.
- A.
Only (I)
- B.
Only (II) and (III)
- C.
Only (I) and (II)
- D.
Only (I) and (III)
Show answer & explanation
Correct answer: B
Concept: When two groups are each declared subsets of the same broader class ('All A are B', 'All C are B'), that alone says nothing about whether A and C overlap - subset membership in a shared superset does not link the subsets to each other. Separately, a universal affirmative 'All A are B' always converts (by limitation) to the particular 'Some B are A'. And combining a particular statement 'Some D are C' with a universal statement on the same middle term 'All C are B' yields the particular conclusion 'Some D are B', which converts simply to 'Some B are D'.
Conclusion I: Papers and bags are each stated only as subsets of books ('All papers are books', 'All bags are books'). No statement links papers to bags directly, so 'Some papers are bags' does not follow - this conclusion fails.
Conclusion II: 'All papers are books' is a universal affirmative, and it converts by limitation to 'Some books are papers'. This conclusion follows directly.
Conclusion III: 'Some purses are bags' is particular, and 'All bags are books' is universal on the shared middle term 'bags'. Combining them gives 'Some purses are books', which converts to 'Some books are purses'. This conclusion follows.
Cross-check with a set diagram: draw books as the outer circle containing two separate inner circles for papers and bags, with no required overlap between them, plus a circle for purses that partially overlaps the bags circle. The purses-bags overlap sits fully inside books, confirming a books-purses overlap, while papers and bags need not touch at all.
So conclusions II and III follow while I does not, matching Only (II) and (III).