Understanding the Exam Copying Scenario

This problem involves logical deduction based on statements made by five students (P, Q, R, S, and T) regarding an exam copying incident. We are given a crucial piece of information: only one student copied, and student S always tells the truth. Our goal is to identify the student who copied in the exam.

Analyzing the Key Information and Student Statements

Let's break down the given facts and statements:

• Key Fact 1: Only one student copied in the exam.
• Key Fact 2: Student S never lies. This means S's statement is always true.

Now, let's list each student's statement:

• Statement of P: "R has copied in the exam."
• Statement of Q: "S has copied in the exam."
• Statement of R: "P did not copy in the exam."
• Statement of S: "Only one of us is telling the truth."
• Statement of T: "R is telling the truth."

Deductive Reasoning to Find the Copier

Since we know that S never lies, S's statement must be absolutely true. S states: "Only one of us is telling the truth."

This is a critical piece of information. If S is telling the truth, and S's truth is that only one person among P, Q, R, S, T is telling the truth, then S must be that one truthful person. This implies that all other students (P, Q, R, and T) must be lying.

Let's proceed by assuming P, Q, R, and T are all lying and see what conclusions we can draw about who copied:

• Analyzing P's statement:
  • P says: "R has copied in the exam."
  • If P is lying, then the opposite of P's statement must be true.
  • Therefore, R did not copy in the exam.
• Analyzing Q's statement:
  • Q says: "S has copied in the exam."
  • If Q is lying, then the opposite of Q's statement must be true.
  • Therefore, S did not copy in the exam. (This aligns perfectly with our initial finding that S never lies, meaning S wouldn't copy.)
• Analyzing R's statement:
  • R says: "P did not copy in the exam."
  • If R is lying, then the opposite of R's statement must be true.
  • Therefore, P copied in the exam.
• Analyzing T's statement:
  • T says: "R is telling the truth."
  • If T is lying, then the opposite of T's statement must be true.
  • Therefore, R is not telling the truth. (This confirms our assumption that R is lying.)

Identifying the Student Who Copied

Based on our consistent deductions:

• We established that R did not copy.
• We established that S did not copy.
• We established that P copied.

Since the problem states that "only one student is known to have copied in the exam," and our analysis consistently points to P as the copier, this conclusion is sound and satisfies all conditions.

Thus, the person who has copied in the exam is P.