In each of the questions below are given few statements followed by two…
2024
In each of the questions below are given few statements followed by two conclusions. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow from the given statements, disregarding commonly known facts.
Statements:
All apartments are huts.
No hut is a building.
All buildings are cottages.
Conclusions:
No apartment is a cottage.
Some buildings being apartments is a possibility.
- A.
Only conclusion I follows
- B.
Only conclusion II follows
- C.
Either conclusion I or conclusion II follows.
- D.
Neither conclusion I nor conclusion II follows.
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Concept:
In categorical syllogisms, an 'All X are Y' statement places every X inside Y, and a 'No X is Y' statement means X and Y share no members at all. A conclusion follows with certainty only when the given statements force it in every possible arrangement consistent with them; a 'possibility' conclusion is valid only when the statements leave that relationship genuinely open, never when a definite all/no relation has already settled it.
Application:
All apartments are huts places every apartment inside the huts group.
No hut is a building removes any overlap between the huts group and the buildings group.
Combining these two: since apartments sit entirely inside huts, and huts share nothing with buildings, apartments cannot overlap with buildings either -- so no apartment is a building is a certain, forced conclusion from the statements.
Conclusion I claims no apartment is a cottage. The only statement touching cottages is all buildings are cottages, which places buildings inside cottages and says nothing about where apartments sit relative to cottages. Since that relationship is never fixed by the statements, Conclusion I is not forced.
Conclusion II claims some buildings being apartments is a possibility. The relation established in the previous step already fixes, with certainty, that no apartment is a building. Once a definite all/no relation is established between two terms, the corresponding some-is-a-possibility reading for that same pair is not left open -- it is ruled out. So Conclusion II fails too.
Cross-check:
Two different diagrams can each satisfy all three statements -- one drawing the apartments circle so it overlaps the cottages circle, another drawing it completely outside the cottages circle. Both stay fully consistent with the statements, so the apartment-cottage relationship can genuinely go either way, confirming Conclusion I is not forced. In every valid diagram, however, the apartments circle and the buildings circle never touch, confirming Conclusion II never holds either.
Result:
Since neither conclusion is forced by the given statements, neither conclusion I nor conclusion II follows.