Syllogism with quantifiers – from ‘‘Some men are educated’’ and ‘‘Educated persons prefer small families’’ decide which conclusions follow about men who prefer small families.

Question

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

Accepted Answer

Premises: (1) Some men are educated. (2) All educated persons prefer small families. Conclusions: (I) All small families are educated. (II) Some men prefer small families. Concept/ApproachChain the premises: Some Men ⟶ Educated and Educated ⟶ Prefer Small Families. Particular + universal yields a particular about men who prefer small families.Test Conclusion I‘‘All small families are educated’’ reverses the given direction. From Educated ⟶ Prefer Small Families, we cannot infer Prefer Small Families ⟶ Educated. Hence I does not follow.Test Conclusion IIFrom (1) some men ∈ Educated, and (2) all Educated ⟶ Prefer Small Families ⇒ those ‘‘some men’’ also prefer small families. Therefore II follows.Common pitfallsConfusing necessary with sufficient conditions. The given universal says being educated is sufficient (not necessary) for preferring small families.Final AnswerOnly conclusion II follows.

Syllogism with quantifiers – from ‘‘Some men are educated’’ and ‘‘Educated persons prefer small families’’ decide which conclusions follow about men who prefer small families.

More Questions from Logical Deduction

Discussion & Comments