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Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements. Statements: All laptops are speakers. All speakers are mics. Conclusions: (I) At least some speakers are laptops. (II) All laptops are mics.
Both conclusions I and II follow
Neither conclusion I nor II follows
Only conclusion II follows
Only conclusion I follows
Both conclusions I and II follow
Since all laptops are speakers and all speakers are mics, the relationship is a nested hierarchy: Laptops inside Speakers inside Mics. Therefore, any subset (Laptops) is naturally contained within the superset (Mics), and the subset is also a part of its immediate container (Speakers).
Since all laptops are speakers and all speakers are mics, the relationship is a nested hierarchy: Laptops inside Speakers inside Mics. Therefore, any subset (Laptops) is naturally contained within the superset (Mics), and the subset is also a part of its immediate container (Speakers).
Analyze Statement 1
All laptops are speakers. This means the set of Laptops is a subset of the set of Speakers (Laptops inside Speakers).
Analyze Statement 2
All speakers are mics. This means the set of Speakers is a subset of the set of Mics (Speakers inside Mics).
Evaluate Conclusions
Combining these: Laptops < Speakers < Mics. Conclusion (I): 'At least some speakers are laptops' is true because if all laptops are speakers, then at least some speakers (those which are laptops) are indeed laptops. Conclusion (II): 'All laptops are mics' is true because laptops are inside speakers, and speakers are inside mics, making all laptops part of the mic set.
B: Incorrect, because both conclusions are valid. C: Incorrect, because both conclusions are valid. D: Incorrect, because both conclusions are valid.
A is correct because all laptops being contained within speakers and speakers being contained within mics logically confirms both that some speakers are laptops and all laptops are mics.
In 'All A are B' statements, always remember that 'Some B are A' is always true (conversion), and 'All A are C' is true if all B are C (transitive property).
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