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.

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.