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?

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:

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:

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.