Some boys are hardworking and no intelligent person is a boy; based on this, which of the given conclusions logically follow?

Introduction / Context:
This syllogism type question involves three sets: boys, hardworking people and intelligent people. You must use the given statements to check which of the provided conclusions are logically forced.

Given Data / Assumptions:

• Statement I: Some boys are hardworking.
• Statement II: No intelligent person is a boy.
• Conclusion I: Some hardworking people are not intelligent.
• Conclusion II: All hardworking people are intelligent.
• Conclusion III: Some intelligent people are not hardworking.

Concept / Approach:
We interpret the statements with Venn diagrams. Some boys are hardworking means there is an overlap between boys and hardworking people. No intelligent person is a boy means the sets intelligent and boys do not overlap at all. We then translate these into implications for the three conclusions.

Step-by-Step Solution:
Step 1: From some boys are hardworking, pick one person who is both a boy and hardworking. Step 2: From no intelligent person is a boy, we know that no boy can belong to the intelligent set. Step 3: Therefore, the boy who is hardworking cannot be intelligent. This directly means some hardworking people are not intelligent, so conclusion I follows. Step 4: Conclusion II says all hardworking people are intelligent, which directly contradicts the existence of at least one hardworking boy who is not intelligent. So conclusion II is false. Step 5: Conclusion III says some intelligent people are not hardworking. The given statements say nothing about whether intelligent people are hardworking or not; they only say intelligent people are not boys. So conclusion III is not forced.

Verification / Alternative check:
Construct an example set. Let boys be {b1, b2}, hardworking be {b1, h1} and intelligent be {i1, i2}. Here b1 is both a boy and hardworking, and intelligent contains no boys. Some hardworking people, such as b1, are not intelligent. However, we could choose to make i1 hardworking or not hardworking without contradicting the statements, so conclusion III is not fixed.

Why Other Options Are Wrong:
Option B includes conclusion III, which is not compelled by the data. Option C treats all conclusions as valid, but conclusions II and III are not. Option D says no conclusion follows, which ignores the clear implication in conclusion I. Option E selects only conclusion II, which is contradicted by the existence of a hardworking boy who is not intelligent.

Common Pitfalls:
A frequent mistake is to assume that if no intelligent person is a boy, then intelligent people must form a completely separate category with some forced properties such as not being hardworking. The statements do not say that. They only exclude overlap with boys, not with hardworking people in general.

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