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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Read the given statement(s) and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statement(s).
Statements:
Some pencils are swans.
No vultures are pencils.
**Conclusions: **
(I) No vultures are swans.
(II) Some swans are not vultures.
Only conclusion (II) follows.
Only conclusion (I) follows.
Neither conclusion (I) nor (II) follows.
Both conclusions (I) and (II) follow.
Only conclusion (II) follows.
Quick Trick: In syllogisms, a Particular Negative ('Some swans are not vultures') can be derived directly from 'Some Pencils are Swans' and 'No Vultures are Pencils'. Swans that are Pencils can NEVER be Vultures!
In syllogisms, a Particular Negative ('Some swans are not vultures') can be derived directly from 'Some Pencils are Swans' and 'No Vultures are Pencils'. Swans that are Pencils can NEVER be Vultures!
Analyze Statement 1 & 2
Statement 1: 'Some pencils are swans' means there is a common region between Pencils and Swans. Statement 2: 'No vultures are pencils' means the set of Vultures has zero overlap with the set of Pencils.
Test Conclusion (I): No vultures are swans
Vultures cannot overlap with Pencils. However, Swans can extend outside the Pencils set into the Vultures set. Since a overlapping relationship between Vultures and Swans is possible without violating statements, 'No vultures are swans' is NOT definitely true in all possible Venn diagrams. Thus, Conclusion (I) does not follow.
Test Conclusion (II): Some swans are not vultures
The portion of Swans that are Pencils (from Statement 1) can NEVER be Vultures (from Statement 2). Therefore, those specific Swans are guaranteed to not be Vultures. Hence, 'Some swans are not vultures' is definitely true in every valid Venn diagram. Thus, Conclusion (II) logically follows.
B: Incorrect because Conclusion (I) is only a possibility, not a definite necessity. C: Incorrect because Conclusion (II) is definitely true and follows logically. D: Incorrect because Conclusion (I) fails to hold true in all possible cases.
A is correct because Conclusion (II) logically follows as the swans that are pencils can never overlap with vultures, whereas Conclusion (I) does not necessarily hold true.
When combining 'Some A are B' and 'No C are A', the guaranteed deduction is always 'Some B are not C' (the portion of B that is A can never be C).