Statement: There is no person who does not possess some virtue, and no person who is entirely free from evil. Conclusions: I. Man is fraught with either virtue or evil (but not both). II. Good and evil points are both present in all of us.
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AIf only conclusion I follows
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BIf only conclusion II follows
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CIf either I or II follows
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DIf neither I nor II follows
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EIf both I and II follow
Answer
Correct Answer: If only conclusion II follows
Explanation
Introduction / Context:The statement encodes two universal claims: (a) everyone has at least some virtue, and (b) no one is entirely devoid of evil. We must test which conclusion represents the logical synthesis of these two universals.
Given Data / Assumptions:
- For every person P: virtue(P) > 0.
- For every person P: evil(P) > 0.
Concept / Approach:Conclusion II is a direct restatement: each person has both good and evil traits. Conclusion I is a mutually exclusive framing (“either…or…”) contradicting the conjunction in the premises. Therefore only II follows.
Step-by-Step Solution:1) Combine the quantifiers: ∀P, virtue(P) and evil(P) are present.2) Evaluate I: “either” excludes simultaneity, which conflicts with the conjunction → I does not follow.3) Evaluate II: explicitly matches the conjunction → II follows.
Verification / Alternative check:If even a single person lacked either virtue or evil, the given universals would be false. Since the statement rules that out, II must hold for everyone.
Why Other Options Are Wrong:“Both/Either” include the contradictory either/or claim; “Neither” ignores the explicit conjunctive logic.
Common Pitfalls:Misreading two universal positives as a disjunction instead of a conjunction.
Final Answer:If only conclusion II follows.