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Question Id : 11885 | Context :NIMCET 2024

Question

You are on an island with two tribes. One tribe always tells the truth, and the other tribe always lies. You meet three individuals from the island A, B and C. Each individual belongs to one of the tribes. You ask each of them the same question “Is B a truthteller?” “Is B a truthteller?” 
 A says, “Yes B is a truth-teller.” 
 B says, “No, I am not a truth-teller” 
 C. Says, “B is a liar” 

 Given that each individual is either a truth-teller or a liar, who is telling the truth?
🎥 Video solution / Text Solution of this question is given below:

Given:

  • A says: "Yes, B is a truth-teller."
  • B says: "No, I am not a truth-teller."
  • C says: "B is a liar."

We need to determine: Who is telling the truth?

Step 1: Assume B is a truth-teller:

If **B is a truth-teller**, then B's statement "No, I am not a truth-teller" would be false, which is a contradiction because a truth-teller cannot lie.

So, **B cannot be a truth-teller**.

Step 2: Assume B is a liar:

If **B is a liar**, then B's statement "No, I am not a truth-teller" must be false, meaning B is indeed a truth-teller. But this is a contradiction because B can't be both a liar and a truth-teller.

Thus, **B must be a liar**.

Step 3: A’s statement analysis:

A says, "Yes, B is a truth-teller." Since we concluded that **B is a liar**, A's statement is false.

This means **A is a liar**.

Step 4: C’s statement analysis:

C says, "B is a liar." Since **B is indeed a liar**, C’s statement is true.

Therefore, **C is a truth-teller**.

✅ Final Answer: C is the truth-teller.

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