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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 oil is paint. All paint is brush. Conclusions: (I) Some brushes are oil. (II) No brush is oil.
Neither conclusion (I) nor (II) follows
Both conclusions (I) and (II) follow
Only conclusion (II) follows
Only conclusion (I) follows
Only conclusion (I) follows
Since all oil is paint and all paint is brush, the entire set of oil is contained within the set of brushes. Therefore, some brushes must be oil, while no brush is oil is definitely false.
Since all oil is paint and all paint is brush, the entire set of oil is contained within the set of brushes. Therefore, some brushes must be oil, while no brush is oil is definitely false.
Analyze the Statements
Given: (1) All oil is paint (Oil is a subset of Paint) and (2) All paint is brush (Paint is a subset of Brush). By transitive logic, all oil is contained within the brush category.
Evaluate Conclusion (I)
Since all oil is paint and all paint is brush, it follows that all oil is brush. If all oil is brush, then 'Some brushes are oil' is logically true.
Evaluate Conclusion (II)
Conclusion (II) states 'No brush is oil'. This contradicts the finding that all oil is brush. Therefore, (II) is false.
A: Incorrect because it states only (II) follows, whereas only (I) follows. B: Incorrect because it states both follow, but (II) is logically impossible. C: Incorrect because it claims neither follows, ignoring the validity of (I).
D is correct because 'All oil is paint' and 'All paint is brush' implies 'All oil is brush', making 'Some brushes are oil' true, while 'No brush is oil' is false.
In All-All type syllogisms, remember that the inner circle is always a subset of the outer circle; thus, 'Some outer is inner' is always true.
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