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.
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AOnly conclusion I follows
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BOnly conclusion II follows
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CBoth conclusion I and II follow
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DNeither conclusion I nor II follow
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ENone of these
Answer
Correct Answer: Only conclusion II follows
Explanation
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:
Step 1: From Premise 1, choose an element d with d ∈ Doctors and d ∈ Teachers.Step 2: From Premise 2, Teachers ⊆ Counsellors, hence d ∈ Counsellors.Step 3: Therefore, some doctors are counsellors (existential conclusion true).Step 4: There is no information guaranteeing the existence of counsellors outside Teachers, so 'Some counsellors are not teachers' is not necessary.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.