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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 coats are jackets. Some coats are sweaters. Conclusions: (I) Some jackets are not coats. (II) Some jackets are sweaters.
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
Represent 'All A are B' as a circle A inside circle B, and 'Some A are C' as an overlapping region, then test if the conclusion holds in all possible scenarios.
Represent 'All A are B' as a circle A inside circle B, and 'Some A are C' as an overlapping region, then test if the conclusion holds in all possible scenarios.
Analyze Statement 1
All coats are jackets: This means the entire circle representing 'coats' is contained within the 'jackets' circle.
Analyze Statement 2
Some coats are sweaters: This means there is an intersection between the 'coats' circle and the 'sweaters' circle.
Evaluate Conclusions
Conclusion I: 'Some jackets are not coats' is not necessarily true because all jackets could be coats. Conclusion II: Since some coats are sweaters and all coats are inside jackets, the part of the coat that is a sweater is automatically part of the jacket. Thus, some jackets must be sweaters.
A: Incorrect because conclusion I is not logically certain. B: Incorrect because conclusion I is not logically certain. C: Incorrect as conclusion II is definitely true. D: Correct as only II follows.
D is correct because 'All coats are jackets' implies that the portion of 'coats' that are 'sweaters' must also be inside the 'jackets' category, making 'Some jackets are sweaters' a logically sound inference.
In syllogisms, avoid assuming extra relationships. If the statement doesn't explicitly restrict a category, treat the possibility that the circles could be identical as valid.
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