Premises — I) Only students can participate in the race. II) Some participants in the race are girls. III) All girl participants in the race are invited for coaching. Question — Which conclusion necessarily follows?
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AAll participants in the race are invited for coaching.
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BAll participants in the race are students.
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CBoth (a) and (b) are necessarily true.
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DNone of the above.
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ESome participants invited for coaching are girls.
Answer
Correct Answer: All participants in the race are students.
Explanation
Introduction / Context:This item mixes set restriction (“only students”) with a subset receiving an invitation (all girl participants). We must pick the conclusion guaranteed by the premises and avoid adding unstated coverage to groups not mentioned explicitly.
Given Data / Assumptions:
- “Only students can participate” → Participant → Student.
- “Some participants are girls” → There exists at least one participant who is a girl.
- “All girl participants are invited” → (Participant ∧ Girl) → Invited.
Concept / Approach:From I), every participant is a student. From II)–III), we know some invitees exist (the girl participants), but nothing is said about non-girl participants. So we can conclude “all participants are students,” but we cannot conclude “all participants are invited.”
Step-by-Step Solution:
Option A: Overreach. Only girl participants are guaranteed invites; other participants may or may not be invited.Option B: Direct consequence of “only students can participate.”Option C: Includes A, which is not guaranteed, so it fails.Option D: Incorrect because B is guaranteed.Option E: While true (some invited are girls), it is not among the original four choices in a standard single-answer format unless we explicitly include it; here, the necessary conclusion requested by the typical pattern is B.Verification / Alternative check:Construct a model where non-girl participants receive no invite; A fails but B remains true. Hence B is the unique necessary conclusion.
Why Other Options Are Wrong:
A assumes all participants invited; not stated.C piggybacks on A.D ignores B’s necessity.Common Pitfalls:Confusing “only students can participate” with “only participants are students.” The former implies participant → student, not the converse.
Final Answer:All participants in the race are students.