Statements: • All Americans are English-speaking. • No Eskimos are English-speaking. Conclusions: I. No Eskimos are Americans. II. No English-speakers are Eskimos. Choose the option that must follow.
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AOnly I follows.
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BNeither I nor II follows.
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COnly II follows.
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DBoth I and II follow.
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EEither I or II follows.
Answer
Correct Answer: Both I and II follow.
Explanation
Introduction / Context:This is a classic use of a universal affirmation combined with a universal exclusion to deduce two symmetric “no overlap” conclusions.
Given Data / Assumptions:
- Americans ⊆ English-speakers.
- Eskimos ∩ English-speakers = ∅.
Concept / Approach:If set X is a subset of Y and a third set Z has empty intersection with Y, then Z must also be disjoint from X. Also, “No Eskimos are English-speaking” is logically equivalent to “No English-speakers are Eskimos.”
Step-by-Step Solution:1) Because Americans ⊆ English-speakers and Eskimos share no members with English-speakers, Eskimos cannot be Americans. Conclusion I is true.2) The premise “No Eskimos are English-speaking” is symmetric: it also entails “No English-speakers are Eskimos.” Conclusion II is true.
Verification / Alternative check:Suppose English-speakers = {e1, e2}, Americans = {e1}, Eskimos = {k1}. Then Americans ⊆ English-speakers and Eskimos disjoint from English-speakers; both conclusions hold.
Why Other Options Are Wrong:Any option denying one of the conclusions contradicts the direct consequences of the premises.
Common Pitfalls:Overlooking the symmetry of “No A are B.” The statement implies two identical non-overlap claims by swapping A and B.
Final Answer:Both I and II follow.