Consider the following three statements by Amar, Akbar and Anthony:
* Amar: "Anthony is a good boy."
* Akbar: "Amar is a liar."
* Anthony: "I am not a good boy."
You know that at least two of them are telling the truth. Who is/are telling the truth?
- AOnly Amar
- BAmar and Akbar
- CAkbar and Anthony
- DAll of them
Solution & Step-by-step Explanation
Let us evaluate the truth values of the statements:
Notice that Amar's statement ("Anthony is a good boy") and Anthony's statement ("I am not a good boy") are direct contradictions. Therefore, exactly one of them must be telling the truth, and the other must be lying.
Case 1: Amar is telling the truth (True).
Then Anthony must be lying (False).
Since Amar is telling the truth, Akbar's statement ("Amar is a liar") must be false.
In this case, we have one True statement (Amar) and two False statements (Akbar, Anthony). This contradicts the given condition that at least two of them are telling the truth.
Case 2: Amar is lying (False).
Then Anthony's statement must be true (True).
Since Amar is lying, Akbar's statement ("Amar is a liar") must be true (True).
In this case, we have two True statements (Akbar and Anthony) and one False statement (Amar). This perfectly satisfies the condition that at least two are telling the truth.
Therefore, Akbar and Anthony are telling the truth.
Notice that Amar's statement ("Anthony is a good boy") and Anthony's statement ("I am not a good boy") are direct contradictions. Therefore, exactly one of them must be telling the truth, and the other must be lying.
Case 1: Amar is telling the truth (True).
Then Anthony must be lying (False).
Since Amar is telling the truth, Akbar's statement ("Amar is a liar") must be false.
In this case, we have one True statement (Amar) and two False statements (Akbar, Anthony). This contradicts the given condition that at least two of them are telling the truth.
Case 2: Amar is lying (False).
Then Anthony's statement must be true (True).
Since Amar is lying, Akbar's statement ("Amar is a liar") must be true (True).
In this case, we have two True statements (Akbar and Anthony) and one False statement (Amar). This perfectly satisfies the condition that at least two are telling the truth.
Therefore, Akbar and Anthony are telling the truth.