In this syllogism style question, two statements are given about authors, teachers and ladies. Treat both statements as true and decide which of the given conclusions, if any, logically follow: Statement I: Some authors are teachers. Statement II: No teacher is a lady. Conclusions: (I) Some teachers are not ladies. (II) Some ladies are not teachers.

Introduction / Context:
This is a logical relations question about the sets authors, teachers and ladies. You must use the two given statements, treat them as completely true, and decide which of the two conclusions must hold. The problem checks whether you correctly interpret negative statements like no teacher is a lady and partial statements like some authors are teachers.

Given Data / Assumptions:

• Statement I: Some authors are teachers.
• Statement II: No teacher is a lady.
• Conclusion I: Some teachers are not ladies.
• Conclusion II: Some ladies are not teachers.
• Some indicates existence of at least one member in the relevant intersection.

Concept / Approach:
Some authors are teachers means there is at least one person who is both an author and a teacher. No teacher is a lady means that the sets teachers and ladies are completely disjoint. We must see what these facts imply about the existence of teachers who are not ladies and about ladies who are not teachers. A conclusion follows only if it is impossible for the statements to be true and the conclusion false at the same time.

Step-by-Step Solution:
Step 1: From statement I, we know that teachers exist because some authors are teachers. So there is at least one teacher. Step 2: From statement II, no teacher is a lady. That means all teachers lie outside the set of ladies. Step 3: Combine the two. Since at least one teacher exists and no teacher is a lady, it follows that at least one teacher is not a lady. This is exactly what conclusion I states. Step 4: Now examine conclusion II: some ladies are not teachers. The statements do not actually assert that any lady exists. They only tell us that the sets teachers and ladies do not overlap. Step 5: It is logically possible, in pure set terms, that there are no ladies at all. In that extreme case, some ladies are not teachers would be false, while the given statements would still be true. Step 6: Because we can imagine a scenario with zero ladies and thus no element satisfying conclusion II, that conclusion is not logically forced by the premises.

Verification / Alternative check:
Construct a simple model. Let teachers be {t1}, authors be {t1, a1} and ladies be an empty set {}. Statement I is satisfied because some authors (t1) are teachers. Statement II is satisfied because no teacher is in the empty set of ladies. In this model, conclusion I holds because t1 is a teacher who is not a lady. But conclusion II fails because there are no ladies at all, so we cannot say some ladies are not teachers. This confirms that only conclusion I follows logically.

Why Other Options Are Wrong:
Option B chooses only conclusion II, which is not guaranteed. Option C says neither conclusion follows, ignoring the clear implication that at least one teacher is not a lady. Option D claims both follow, but we have shown that conclusion II can be false in a model where the statements hold. Option E suggests that exactly one of them (without specifying) must follow, but the exam expects you to identify conclusion I as the only valid one.

Common Pitfalls:
One common mistake is to assume that categories like ladies must contain some members just because the word is used, and then derive some ladies are not teachers from the disjointness. Formal logic does not automatically assume non empty sets unless specified. Another pitfall is to overlook the explicit existence provided by some authors are teachers, which guarantees that teachers exist and leads directly to conclusion I.

Final Answer:
The correct logical result is that only conclusion I follows from the given statements.