Statement(s): Some bells are alarms. Some alarms are bow. Conclusions: I. Some…
2023
Statement(s):
Some bells are alarms.
Some alarms are bow.
Conclusions:
I. Some bells are bow.
II. Some alarms are cats.
- A.
Both conclusion I and conclusion II follow
- B.
Neither conclusion I nor conclusion II follows
- C.
Only conclusion II follows.
- D.
Only the conclusion I follows.
Show answer & explanation
Correct answer: B
Concept: When both premises of a syllogism are particular ("Some X are Y"), the shared middle term is undistributed in each, so the two "some" portions referred to need not overlap, and no definite conclusion linking the outer terms can be drawn. A conclusion can also never validly introduce a term absent from both premises.
Application:
Premise 1, "Some bells are alarms," and Premise 2, "Some alarms are bow," are both particular — neither fixes the whole class of alarms.
Because "alarms" is undistributed in both, the alarms overlapping with bells in Premise 1 need not be the same alarms overlapping with bow in Premise 2.
A valid arrangement exists where both premises hold yet bells and bow share no member — so Conclusion I ("Some bells are bow") is not a necessary consequence of the premises.
Conclusion II ("Some alarms are cats") introduces "cats," a term found in neither premise, so it can never be validly concluded.
Cross-check: since a case exists where the premises are true but each conclusion is false, neither conclusion is logically guaranteed — so the correct choice is that neither conclusion I nor conclusion II follows.