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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 shirts are pants. Some pants are coats. Conclusions: (I) Some pants are not shirts. (II) Some shirts are coats.
Both conclusions I and II follow
Only conclusion II follows
Neither conclusion I nor II follows
Only conclusion I follows
Neither conclusion I nor II follows
In syllogisms with 'Some' relations, negative conclusions like 'Some X are not Y' are only true if they are explicitly stated or forced by a 'No' relation. Otherwise, they are treated as 'Possible' rather than 'Certain' (Follows).
In syllogisms with 'Some' relations, negative conclusions like 'Some X are not Y' are only true if they are explicitly stated or forced by a 'No' relation. Otherwise, they are treated as 'Possible' rather than 'Certain' (Follows).
Analyze Statement 1
Statement: 'Some shirts are pants'. This implies an intersection between the set of shirts and the set of pants.
Analyze Statement 2
Statement: 'Some pants are coats'. This implies an intersection between the set of pants and the set of coats.
Evaluate Conclusion I
'Some pants are not shirts' is not necessarily true because the statements do not provide any negative information about pants relative to shirts; they could potentially overlap entirely.
Evaluate Conclusion II
'Some shirts are coats' is not necessarily true. While shirts overlap with pants and pants overlap with coats, the direct relationship between shirts and coats is unknown/undetermined.
A: Incorrect; Conclusion I is a possibility, not a logical necessity. B: Incorrect; neither conclusion follows. D: Incorrect; Conclusion II is not necessarily true.
C is correct because both conclusions fail to logically follow as they represent possibilities rather than definitive certainties based on the provided statements.
In logical reasoning tests, if the conclusion introduces a new relation that isn't directly mentioned or forced by the statements, it is usually invalid.
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