Consider the following three statements: 1. Only students can participate in the race. 2. Some participants in the race are girls. 3. All girl participants in the race are invited for coaching. Which one of the following conclusions can be drawn from the above statements?

To solve syllogism and logical reasoning questions in the UPSC CSAT, it is essential to break down each statement into its logical components, often using Venn diagrams or categorical logic.

Here is the step-by-step breakdown of the problem:

1. Breakdown of the Statements

• Statement 1: "Only students can participate in the race."
  • Logical Interpretation: This is a restrictive statement. It means that if someone is a participant, they must be a student. It establishes that the set of "Participants" is a subset of the set of "Students."
  • Relationship: Participants $\subseteq$ Students.
• Statement 2: "Some participants in the race are girls."
  • Logical Interpretation: There is an overlap between the set of "Participants" and the set of "Girls."
• Statement 3: "All girl participants in the race are invited for coaching."
  • Logical Interpretation: Within the group of participants, those who are girls are a subset of those "Invited for coaching."

2. Step-by-Step Reasoning

Step 1: Analyze Statement 1 (The "Only" Rule) In logic, the statement "Only A are B" is equivalent to "All B are A." Therefore, "Only students (A) can participate (B)" means "All participants are students." This establishes a definitive boundary: No non-student can be a participant.

Step 2: Combine with Statement 2 We know some participants are girls. Based on Step 1, since all participants are students, these specific "girl participants" are also students.

Step 3: Combine with Statement 3 We know those girl participants are invited for coaching. This tells us some students (the ones who are girls and participated) are invited for coaching.

3. Evaluating the Options

Option A: All participants in the race are invited for coaching.

• Analysis: Statement 3 says only the girl participants are invited for coaching. We have no information about the boy participants. They might be invited, or they might not. We cannot conclude "All" based on the given data.
• Verdict: Incorrect.

Option B: All students are invited for coaching.

• Analysis: Statement 1 tells us that participants must be students, but it does not say that all students are participants. Furthermore, even among participants, only the girls are definitely invited for coaching. Therefore, we cannot say anything about "All students."
• Verdict: Incorrect.

Option C: All participants in the race are students.

• Analysis: This is a direct logical derivation of Statement 1 ("Only students can participate"). If the race is restricted only to students, then it is a logical necessity that every single person participating is a student.
• Verdict: Correct.

Option D: None of the statements (a), (b) and (c) given above is correct.

• Analysis: Since Option C is a direct and valid logical conclusion, this option is eliminated.
• Verdict: Incorrect.

4. Summary for Aspirants

In UPSC CSAT, "Only" is a powerful keyword. When you see "Only A are B", immediately translate it to "All B are A" in your mind.

• Statement: Only students (A) participate (B).
• Conclusion: All participants (B) are students (A).

This matches Option C perfectly. The other statements about girls and coaching act as "distractors" to test if you can maintain focus on the primary constraint established in the first sentence.