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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: Some cars are bikes. All bikes are trucks. Conclusions: (I) Some trucks are cars. (II) All trucks are cars.
Only conclusion (II) follows
Only conclusion (I) follows
Neither conclusion (I) nor (II) follows
Both conclusions (I) and (II) follow
Only conclusion (I) follows
Convert statements to standard syllogism representations: 'Some cars are bikes' (I) and 'All bikes are trucks' (A). The intermediate term 'bikes' links them, allowing us to derive 'Some cars are trucks' (I) or its converse 'Some trucks are cars' (I).
Convert statements to standard syllogism representations: 'Some cars are bikes' (I) and 'All bikes are trucks' (A). The intermediate term 'bikes' links them, allowing us to derive 'Some cars are trucks' (I) or its converse 'Some trucks are cars' (I).
Analyze Statement 1
Some cars are bikes. This establishes a partial overlap between the set of Cars and the set of Bikes.
Analyze Statement 2
All bikes are trucks. This means the entire set of Bikes is contained within the set of Trucks.
Evaluate Conclusion (I)
Some trucks are cars. Since some cars are bikes and all bikes are trucks, the region where cars and bikes overlap is also inside trucks. Thus, some trucks are indeed cars. Conclusion (I) follows.
Evaluate Conclusion (II)
All trucks are cars. The statements only guarantee that some cars are bikes and bikes are trucks; they do not state that all trucks are cars. Conclusion (II) does not follow.
A: Only conclusion (I) follows - Correct. C: Neither conclusion (I) nor (II) follows - Incorrect because conclusion (I) is logically derived. D: Both conclusions (I) and (II) follow - Incorrect because conclusion (II) cannot be deduced universally. B in official key corresponds to Only conclusion (I) follows.
B is correct because conclusion (I) logically follows from the given statements while conclusion (II) does not.
In categorical syllogisms involving 'Some' and 'All', remember that 'Some A are B' always implies 'Some B are A' (conversion).
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