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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 gold are silver. Some silver are diamonds. Conclusions: (I) Some diamonds are gold. (II) Some silver are gold.
Both conclusions (I) and (II) follow
Only conclusion (I) follows
Neither conclusion (I) nor (II) follows
Only conclusion (II) follows
Only conclusion (II) follows
Draw overlapping circles for 'Gold', 'Silver', and 'Diamonds'. Check direct intersections to see which conclusions are definitely true.
Draw overlapping circles for 'Gold', 'Silver', and 'Diamonds'. Check direct intersections to see which conclusions are definitely true.
Analyze Statement 1
Statement 1 states: 'Some gold are silver.' This means there is a positive intersection between the set of Gold and the set of Silver.
Analyze Statement 2
Statement 2 states: 'Some silver are diamonds.' This means there is a positive intersection between the set of Silver and the set of Diamonds.
Evaluate Conclusion I
Conclusion I states: 'Some diamonds are gold.' Since there is no direct statement linking Gold and Diamonds (they only both intersect with Silver independently), no definite relationship between Gold and Diamonds can be established. Thus, Conclusion I does not follow.
Evaluate Conclusion II
Conclusion II states: 'Some silver are gold.' Since Statement 1 says 'Some gold are silver', its converse 'Some silver are gold' is unconditionally true. Thus, Conclusion II follows.
A: Both conclusions follow is incorrect because Conclusion I is indefinite. B: Only conclusion (I) follows is incorrect because Conclusion I does not follow. C: Neither conclusion follows is incorrect because Conclusion II is definitely true. D: Only conclusion (II) follows is correct.
D is correct because conclusion II directly follows from the converse of the first statement, while conclusion I cannot be definitively established due to lack of a direct link between gold and diamonds.
In syllogisms, never assume a direct relationship between two independent terms (Gold and Diamonds) just because both share a common relation with a third term (Silver) unless explicitly stated.
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