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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: No dogs are pigs. All pigs are stones. Conclusions: (I) Some stones are pigs. (II) No stones are dogs.
Both conclusions (I) and (II) follow
Only conclusion (I) follows
Neither conclusion (I) nor (II) follows
Only conclusion (II) follows
Only conclusion (I) follows
Draw standard overlapping Venn diagram circles for Dogs, Pigs, and Stones. Since No dogs are pigs and All pigs are stones, some stones are definitely pigs, and no stones (which are pigs) can be dogs.
Draw standard overlapping Venn diagram circles for Dogs, Pigs, and Stones. Since No dogs are pigs and All pigs are stones, some stones are definitely pigs, and no stones (which are pigs) can be dogs.
Analyze Statement 1
No dogs are pigs. This means the set of Dogs and the set of Pigs are completely disjoint.
Analyze Statement 2
All pigs are stones. This means the entire set of Pigs is enclosed inside the set of Stones.
Evaluate Conclusion I
Since all pigs are stones, some part of stones consists of pigs. Thus, 'Some stones are pigs' is definitely true (follows).
Evaluate Conclusion II
No stones are dogs is false because the portion of stones that contains pigs cannot intersect with dogs, but other parts of stones outside pigs can potentially intersect with dogs. Thus, conclusion II does not logically follow.
A: Both conclusions do not follow because conclusion II is invalid. C: Neither conclusion does not follow since conclusion I is correct. D: Only conclusion II does not follow.
B is correct because only conclusion (I) logically follows from the given statements.
In syllogism problems with universal and particular statements, always draw all possible Venn diagram cases to test whether negative conclusions are definitively true or merely possible.
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