Syllogism reasoning with two premises: ‘‘All men are married’’ and ‘‘Some men are educated’’ — determine which logical conclusions about the overlap between married persons and educated persons necessarily follow.

Question

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

Curioustab · Accepted Answer

Evaluate the two conclusions based on classical syllogism rules. Premise 1: All men are married. This means Men ⊆ Married. Premise 2: Some men are educated. This means Men ∩ Educated is non empty. Conclusions to test: I. Some married are educated. II. Some educated are married. Concept/ApproachUse set inclusion and particular existence. If a non empty subset of Men is also Educated and all Men are inside Married, that same subset lies inside Married as well.Step by Step derivation1) From Men ⊆ Married and Men ∩ Educated ≠ ∅, map the existing elements in Men ∩ Educated into Married. Therefore Married ∩ Educated ≠ ∅.2) Conclusion I follows: Some married are educated.3) Symmetrically, the same non empty set shows Educated ∩ Married ≠ ∅, which reads as: Some educated are married. Hence Conclusion II follows.Verification/AlternativePick an example world with Men = {m1, m2}, Married = {m1, m2, x}, Educated = {m1, y}. Clearly m1 witnesses both conclusions.Common pitfallsConfusing particular with universal. We only assert existence of overlap, not that all married are educated or vice versa.Final AnswerBoth I and II follow.