Reasoning with ‘‘most’’ and ‘‘some’’ quantifiers: given ‘‘Most teachers are boys’’ and ‘‘Some boys are students,’’ identify which conclusions are logically certain.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Premises: (1) Most teachers are boys. (2) Some boys are students. Conclusions: (I) Some students are boys. (II) Some teachers are students. Concept/Approach‘‘Some boys are students’’ is already a particular statement about overlap; (I) restates it directly. But there is no guaranteed overlap between Teachers and Students given only these two statements.Evaluate Conclusion IPremise (2) explicitly asserts an element in Boys∩Students. Therefore I follows.Evaluate Conclusion IIFrom ‘‘Most teachers are boys’’ we know Teachers ⊆ Boys to a large extent, but not that any of those teacher-boys are among the ‘‘some’’ boys who are students. Hence II does not necessarily follow.Common pitfallsAssuming transitivity for ‘‘most’’ and ‘‘some.’’ Without explicit intersection, Teacher∩Student might be empty.Final AnswerOnly conclusion I follows.

Reasoning with ‘‘most’’ and ‘‘some’’ quantifiers: given ‘‘Most teachers are boys’’ and ‘‘Some boys are students,’’ identify which conclusions are logically certain.

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