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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: No bike is a car. All cars are planes. Conclusions (I) No plane is a bike. (II) All planes are cars.
Only conclusion (II) follows
Neither conclusion (I) nor (II) follows
Only conclusion (I) follows
Both conclusions (I) and (II) follow
Neither conclusion (I) nor (II) follows
Convert statements into set inclusion/exclusion rules: No Bike is Car (B тИй C = тИЕ), All Cars are Planes (C тКЖ P). Check conclusions against these rules.
Convert statements into set inclusion/exclusion rules: No Bike is Car (B тИй C = тИЕ), All Cars are Planes (C тКЖ P). Check conclusions against these rules.
Analyze Statement 1
No bike is a car. This means the set of Bikes and the set of Cars are completely disjoint (No intersection).
Analyze Statement 2
All cars are planes. This means the entire set of Cars is enclosed inside the set of Planes.
Evaluate Conclusion I
No plane is a bike. Since some part of the Planes set contains Cars (which are disjoint from Bikes), it is possible that some Planes are Bikes or some are not. Thus, this does not definitively follow.
Evaluate Conclusion II
All planes are cars. The statement only states all cars are planes, which does not imply the reverse. Thus, this conclusion does not follow.
A: Only conclusion (II) follows is incorrect because conclusion II is a reverse universal statement which is false. C: Only conclusion (I) follows is incorrect as neither conclusion is definitively true. D: Both conclusions follow is incorrect because neither statement establishes the required conditions.
B is correct because neither conclusion logically follows from the given statements based on set theory rules.
Remember that 'All A are B' does not mean 'All B are A' (conversion of universal affirmative is invalid). Similarly, absolute negative relations only apply between the exact stated terms unless bridged by a definite inclusion.
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