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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 tigers are lions. Some lions are cheetahs. Conclusions: I. Some lions are tigers. II. Some tigers are cheetahs.
Only conclusion II follows
Neither conclusion I nor II follows
Both conclusions I and II follow
Only conclusion I follows
Only conclusion I follows
In syllogisms with 'Some' statements, if the terms are not directly linked by a transitive chain, no conclusion can be drawn between those terms.
In syllogisms with 'Some' statements, if the terms are not directly linked by a transitive chain, no conclusion can be drawn between those terms.
Analyze Statement 1
Statement: Some tigers are lions. This implies a partial overlap between the set of tigers and the set of lions.
Analyze Statement 2
Statement: Some lions are cheetahs. This implies a partial overlap between the set of lions and the set of cheetahs.
Evaluate Conclusion I
Conclusion I: Some lions are tigers. This is a direct converse of the first statement 'Some tigers are lions'. Therefore, it is logically true.
Evaluate Conclusion II
Conclusion II: Some tigers are cheetahs. While tigers overlap with lions and lions overlap with cheetahs, there is no necessary link provided between tigers and cheetahs. Therefore, it does not follow.
A: Incorrect as it says 'Only conclusion II follows'. B: Incorrect as it says 'Neither conclusion follows'. C: Incorrect as it says 'Both conclusions follow'. D: This correctly identifies that only I follows.
D is correct because 'Some lions are tigers' is the direct conversion of 'Some tigers are lions', while 'Some tigers are cheetahs' cannot be inferred from the given statements as no direct relationship between tigers and cheetahs is defined.
Always remember that in syllogisms, 'Some A are B' implies 'Some B are A'. Do not assume any relationship between the first and third terms if the middle term does not bridge them definitively.
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