In the following question, some statements are given followed by conclusions…
2021
In the following question, some statements are given followed by conclusions based on those statements. Taking the statements to be true, even if they seem to be at variance with commonly known facts, read all the conclusions and decide which conclusion logically follows.
Statements:
I. Some P are K.
II. No S is P.
Conclusions:
I. No P is S.
II. All S are K.
- A.
Only conclusion I follows
- B.
Only conclusion II follows
- C.
Both conclusions I and II follow
- D.
Neither conclusion follows
Attempted by 58 students.
Show answer & explanation
Correct answer: A
Concept: In categorical syllogisms, a universal negative statement ('No A is B') always converts simply to its mirror form, 'No B is A' — this conversion is guaranteed regardless of any other statement. Separately, a conclusion linking two terms is valid only when the premises connect those exact terms, directly or through a shared middle term; if no such connection exists, no conclusion about that pair can be drawn.
Statement II, 'No S is P,' is a universal negative relating S and P.
By simple conversion, 'No S is P' also means 'No P is S' — this is exactly Conclusion I, so Conclusion I follows.
Statement I, 'Some P are K,' relates P and K; Statement II relates S and P. Together they connect P to both K and S, but never connect S directly to K.
Since no premise or valid conversion links S to K, Conclusion II, 'All S are K,' has no support and does not follow.
Cross-check with a model: let P = {1, 2}, K = {2, 3} (so 'Some P are K' holds, since 2 is common to both), and S = {4, 5} (so 'No S is P' holds, since S and P share nothing). Here S and K also share nothing, so 'All S are K' is false even though both original statements hold — confirming that Conclusion II is never guaranteed.
Therefore, only Conclusion I follows; Conclusion II does not follow from the given statements.