Statements I and II are followed by conclusions (a) and (b). Assuming the…

Concept

In categorical reasoning, an existential statement such as “Some R are G” guarantees only that at least one member lies in the overlap of R and G.

Two existential premises with the same subject class may refer to different members. An overlap cannot be transferred from one predicate to another unless the premises explicitly connect those predicates.

Application

1. Let R denote religious people, G morally good people, and A rational people. Statement I gives a member of R ∩ G, while statement II gives a member of R ∩ A; the two members need not be the same.

2. Conclusion (a) would require the rational members of R to be morally good. The premises provide no relation between A and G, so this claim is not forced.

3. Conclusion (b) would require the non-rational members of R to be outside G. The premises provide no such exclusion, so this claim is also not forced.

Cross-check by counterexample

Consider two people with the following memberships:

P is religious and morally good but not rational; Q is religious and rational but not morally good. Both statements are true, while (a) fails because of Q and (b) fails because of P.

Result

Therefore, neither (a) nor (b) logically follows.