Statements: All pens are books. Some books are bags. Conclusions: I. Some pens are bags. II. Some bags are books. Which conclusions follow?
Only II follows. 'Some books are bags' can be reversed to 'some bags are books', so II is certain. I is not certain: the books that are bags might be entirely outside the pens, so pens and bags need not overlap.
Explain it simply
Treat each statement as circles (a Venn diagram) and ask: is the conclusion true in every possible drawing? If you can draw even one valid picture where it fails, it does not follow. A conclusion that is merely possible is not enough. "Some A are B" can always be flipped to "some B are A".
Example
Statements: All pens are books. Some books are bags.
[ Books ( Pens ) ]
[ overlap ] with Bags, placed away from Pens- Pens sit entirely inside Books.
- Bags overlap Books somewhere. That overlap can be in the part of Books with no pens.
- Conclusion I (some pens are bags): in the drawing above no pen is a bag, so I is not certain. Does not follow.
- Conclusion II (some bags are books): this is just 'some books are bags' reversed. Follows.
Answer: only II follows.
Rule of thumb: "All A are B" plus "Some B are C" gives no definite link between A and C, because the middle term (B) is not fully covered in either statement.
What to say in the interview
"Pens are inside books, and bags overlap books, but that overlap could avoid the pens entirely, so I is only a possibility. II is the converse of the second statement, so it follows. Only II."
Common mistakes
- Accepting a conclusion because it is possible rather than certain.
- Converting 'All A are B' into 'All B are A'; it only converts to 'Some B are A'.