Syllogism – Two-premise categorical logic: Statements: 1) All authors are learned people. 2) Some doctors are authors. Conclusions to test: I) Some doctors are learned people. II) Some learned people are doctors. Select the option that correctly identifies which conclusions logically follow.

Introduction / Context:
This problem tests basic categorical syllogism with two premises and conclusions that must follow necessarily in all valid interpretations. The terms are Authors, Learned people, and Doctors. We must avoid real-world knowledge and rely only on logical structure.

Given Data / Assumptions:

• Premise 1: All Authors are Learned (Authors ⊆ Learned).
• Premise 2: Some Doctors are Authors (∃x: Doctor ∧ Author).
• Standard syllogism rules; no hidden assumptions beyond existence stated by “some”.

Concept / Approach:
Use set/venn reasoning. From a universal premise (All A are L) and a particular premise (Some D are A), we can push membership through the subset relation.

Step-by-Step Solution:
Step 1: From Premise 2, choose an element x that is Doctor and Author.Step 2: Apply Premise 1 to x. Since all Authors are Learned, x is Learned.Step 3: Therefore x is both Doctor and Learned, proving “Some Doctors are Learned.” (Conclusion I)Step 4: The same witness x also proves “Some Learned are Doctors.” (Conclusion II)

Verification / Alternative check:
A standard Venn diagram with Authors inside Learned and an overlapping Doctors region intersecting Authors immediately shows a non-empty overlap between Doctors and Learned.

Why Other Options Are Wrong:

• Only I follows: Incorrect, because II also follows by the same witness.
• Only II follows: Incorrect for the same reason; I follows as well.
• Neither follows: False; we have a concrete element proving both.
• None of these: Not applicable since “Both I and II follow” is available and correct.

Common Pitfalls:
Confusing “some” with “all,” or thinking that the converse of a universal requires a separate proof. Here, the particular premise supplies existence, and the universal moves that element into Learned.

Final Answer:
Both I and II follow.