Syllogism — University professors and doctorate degrees: Statements: • All university professors have a doctorate degree. • X is a lady professor. Conclusions to test: I. X does not have a doctorate degree. II. Only men professors have a doctorate degree. Decide which conclusion(s) logically follow(s) from the statements.

Introduction / Context:
This item tests categorical syllogism logic using a universal affirmative premise and an individual case. We must determine which stated conclusions necessarily follow from the given premises without adding outside facts or stereotypes.

Given Data / Assumptions:

• All university professors have a doctorate degree (Professor ⊆ Doctorate-holders).
• X is a professor; additionally, X is a woman ('lady professor').
• Conclusions must be necessary, not merely plausible.

Concept / Approach:
Use set inclusion. From “All professors have a doctorate,” Professor ⊆ Doctorate. Instantiating for X yields X ∈ Doctorate. The premise says nothing about gender restrictions on doctorate holders.

Step-by-Step Solution:
1) From the universal rule, every professor must have a doctorate.2) Since X is a professor, X must have a doctorate.3) Conclusion I (“X does not have a doctorate”) contradicts step 2 and therefore does not follow.4) Conclusion II (“Only men professors have a doctorate”) introduces a gender restriction not present in the premises; it does not follow.

Verification / Alternative check:
Construct a model where professors of any gender all have doctorates; I becomes false and II is not forced.

Why Other Options Are Wrong:
“Only I follows” is wrong because I contradicts the premise. “Only II follows” is wrong because gender is never constrained. “Both follow” is impossible (I is false).

Common Pitfalls:
Assuming extra information about gender from social context, or misreading “All” as “Only men.”

Final Answer:
Neither I nor II follows.