Syllogism – Shared superset without guaranteed overlap: Statements: (a) All poets are intelligent. (b) All singers are intelligent. Conclusions: I) All singers are poets. II) Some intelligent persons are not singers.

Introduction / Context:
Two different groups lie inside the same superset (Intelligent). The trap is to infer overlap where none is stated.

Given Data / Assumptions:

• Poet ⊆ Intelligent.
• Singer ⊆ Intelligent.
• No premise about Poet–Singer intersection or about the size of Intelligent.

Concept / Approach:
(I) “All singers are poets” is unjustified: two distinct subsets of a superset can be disjoint. (II) “Some intelligent persons are not singers” is also not compelled: it is possible (though unlikely in reality) that every intelligent person is a singer in some models. Syllogism evaluates necessity across all models, not plausibility.

Step-by-Step Solution:
Construct Model A: Poets and Singers are disjoint proper subsets of Intelligent. (I) fails; (II) holds here but is not necessary.Construct Model B: Intelligent = Singers, with Poets ⊆ Singers. (I) may still fail, but (II) fails because every Intelligent is a Singer. Because conclusions can flip, neither is necessary.

Verification / Alternative check:
Necessity requires truth in all valid models. Since countermodels exist for both I and II, neither follows.

Why Other Options Are Wrong:
They claim necessity where only possibility exists.

Common Pitfalls:
Assuming “shared superset” implies overlap or non-overlap without explicit statements.

Final Answer:
Neither conclusion I nor II follows.