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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 kings are servants. Some servants are fighters. Conclusions: (I) Some fighters are kings. (II) All servants are kings.
Neither conclusion (I) nor (II) follows
Both conclusions (I) and (II) follow
Only conclusion (I) follows
Only conclusion (II) follows
Neither conclusion (I) nor (II) follows
Translate statements into overlapping circles. A positive particular conclusion (Some) is true if there is an intersection between the terms, while a universal affirmative (All) requires complete containment which is not guaranteed.
Translate statements into overlapping circles. A positive particular conclusion (Some) is true if there is an intersection between the terms, while a universal affirmative (All) requires complete containment which is not guaranteed.
Step 1: Analyze Statement 1
Some kings are servants. This indicates a partial overlap between the set of Kings and the set of Servants.
Step 2: Analyze Statement 2
Some servants are fighters. This indicates a partial overlap between the set of Servants and the set of Fighters.
Step 3: Evaluate Conclusion I
Some fighters are kings. There is no direct information given connecting fighters and kings. While it is a possibility, it is not definitely true in all cases. Hence, conclusion I does not follow.
Step 4: Evaluate Conclusion II
All servants are kings. The statement only says 'Some kings are servants', which does not imply that all servants are kings. Hence, conclusion II does not follow.
B: Both conclusions follow is incorrect because neither conclusion is logically definite. C: Only conclusion (I) follows is incorrect as fighters and kings have no guaranteed overlap. D: Only conclusion (II) follows is incorrect since all servants are not necessarily kings.
A is correct because neither conclusion logically follows with absolute certainty from the given statements.
In syllogisms, a positive particular statement ('Some A are B') never implies universal certainty ('All B are A'), nor does it establish a direct link to a third independent term ('C') unless a bridge statement is provided.
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