Syllogism — Given: Some doctors are teachers. All teachers are counsellors. Determine which conclusions follow: I) Some counsellors are not teachers. II) Some doctors are counsellors.

Introduction / Context:This problem involves set inclusions. We must check if the provided conclusions necessarily follow from the premises about doctors, teachers, and counsellors.

Given Data / Assumptions:

• Premise 1: Some doctors are teachers (Doctors ∩ Teachers is non-empty).
• Premise 2: All teachers are counsellors (Teachers ⊆ Counsellors).

Concept / Approach:Use transitivity of subset and existence from 'some'. If some doctors are teachers and all teachers are counsellors, then those doctor-teachers are counsellors, implying 'Some doctors are counsellors'. However, 'Some counsellors are not teachers' introduces a negative that is not supported by the premises.

Step-by-Step Solution:

Verification / Alternative check:A model where Teachers = Counsellors makes I false but II true. As long as at least one doctor is a teacher, II follows.

Why Other Options Are Wrong:

• Only I follows: unsupported; could be false if Counsellors equals Teachers.
• Both follow: I is not necessary.
• Neither follows: II must follow.

Common Pitfalls:Assuming a larger set necessarily contains elements outside a subset without evidence.

Final Answer:Only conclusion II follows.