Syllogism — Applying a universal statement to an individual case Statements: • All boys are tall. • Rajiv is a boy. Conclusions: I) Rajiv is tall. II) Rajiv is not tall. Choose the correct evaluation.
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AOnly Conclusion I follows
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BOnly Conclusion II follows
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CBoth Conclusion I and Conclusion II follow
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DNeither Conclusion I nor Conclusion II follows
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ENone of these
Answer
Correct Answer: Only Conclusion I follows
Explanation
Introduction / Context:Here a universal statement about a category is applied to a named individual within that category. The test is to push the inclusion correctly and reject the contradiction.
Given Data / Assumptions:
- All Boys ⊆ Tall.
- Rajiv ∈ Boys.
Concept / Approach:If every boy is tall and Rajiv is a boy, then Rajiv must be tall. Any statement that asserts the contrary directly conflicts with the universal premise.
Step-by-Step Solution:
Step 1: Substitute: since Rajiv ∈ Boys and Boys ⊆ Tall, infer Rajiv ∈ Tall.Step 2: Compare the two proposed conclusions. I matches the derivation; II contradicts it.Verification / Alternative check:In a Venn diagram, place Rajiv in the Boys circle, which is inside the Tall circle. The placement makes I true and II impossible.
Why Other Options Are Wrong:
- Only II follows: contradicts the universal premise.
- Both follow / Neither follow: cannot be, because I is forced and II is negated by the same premise.
Common Pitfalls:Overcomplicating a straightforward categorical substitution; suspecting exceptions when none are allowed by the statement “All.”
Final Answer:Only Conclusion I follows.