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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 legs are hands. Some legs are ears. Conclusions: (I) Some hands are ears. (II) Some ears are legs.
Only conclusion II follows
Only conclusion I follows
Neither conclusion I nor II follows
Both conclusions I and II follow
Both conclusions I and II follow
All legs are hands means legs are inside the hands circle. Some legs are ears means the ears circle partially overlaps the legs circle. Since legs are inside hands, the overlapping ears must also overlap the hands.
All legs are hands means legs are inside the hands circle. Some legs are ears means the ears circle partially overlaps the legs circle. Since legs are inside hands, the overlapping ears must also overlap the hands.
Analyze Statements
1. 'All legs are hands' means the entire set of legs is a subset of hands. 2. 'Some legs are ears' means there is an intersection between the legs set and the ears set.
Evaluate Conclusion I
Since some legs are ears, and all legs are hands, those specific legs that are ears must also be inside the hands group. Thus, 'Some hands are ears' is true.
Evaluate Conclusion II
The statement 'Some legs are ears' directly implies the existence of a common region between ears and legs. Thus, 'Some ears are legs' is true.
A, B, and C are incorrect because they imply only one or neither conclusion follows, whereas both logically follow from the given premises.
D is correct because both conclusions are logically derived from the Venn diagram overlap: the intersection of 'legs and ears' is inherently contained within the 'hands' circle.
In Syllogism, always remember that 'Some A are B' is the same as 'Some B are A'. Converting the statement early can save time.
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