Logical deduction – "only toppers get IIT admission": Only the toppers in Class 12 get admitted to IITs. Which pair is logically consistent/consequential? (i) Sid got admission in IIT. (ii) Sid is a topper in Class 12. (iii) Sid did not get admission in IIT. (iv) Sid did not top in anything.
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A(iii) (iv)
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B(i) (ii)
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C(ii) (i)
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D(iv) (iii)
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ENone of these
Answer
Correct Answer: (i) (ii)
Explanation
Introduction / Context:"Only toppers get admitted" means admission implies topper (Admission → Topper). It does not say every topper must get admission.
Given Data / Assumptions:
- Rule: If someone is admitted to an IIT, they are a topper.
- No claim that every topper is admitted.
Concept / Approach:We check which pair aligns with Admission → Topper and avoids invalid converses.
Step-by-Step Solution:
(i) Admission true ⇒ (ii) Topper must be true; hence (i) (ii) is a valid consequence.Pairs like (iii) (iv): "no admission ⇒ not topper" is the inverse fallacy and is not entailed.Verification / Alternative check:A Venn view: IIT-admitted is a subset of toppers. Anyone inside admitted is inside topper.
Why Other Options Are Wrong:(iii) (iv) and (iv) (iii) commit the inverse error. (ii) (i) lists the same two truths but the consequence is specifically Admission ⇒ Topper; (i) (ii) cleanly expresses it.
Common Pitfalls:Assuming the converse (Topper ⇒ Admission) which is not stated.
Final Answer:(i) (ii)