# All people in a certain are either ‘Knights’ or ‘Knaves’ and each person knows every other person’s identity. Knights NEVER lie, and knaves ALWAYS lie

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All people in a certain are either ‘Knights’ or ‘Knaves’ and each person knows every other person’s identity. Knights NEVER lie, and knaves ALWAYS lie.

P says “Both of us are knights”, Q says “None of us are knaves”.

Which one of the following can be logically inferred from the above?
1. Both P and Q are knights
2. P is a knight; Q is a knave
3. Both P and Q are knaves
4. The identities of P, Q cannot be determined

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Correct Answer - Option 4 : The identities of P, Q cannot be determined

Here let’s check each option,

a) Both P and Q are knights → If both are knights then both must say the truth.

P says “Both of us are knights”, Q says “None of us are knaves”.

Thus can be true.

b) P is a knight; Q is a knave → If P is a knight then P must say the truth.

P says “Both of us are knights”, but Q says “None of us are knaves”.

This cannot be true.

c) Both P and Q are knaves → If both are knaves then both must lie.

P says “Both of us are knights”, Q says “None of us are knaves”.

Thus can be true.

Thus both P and Q are knights or both P and Q are knaves.

Thus identities of P, Q cannot be determined.

Alternate Solution

Essentially both P and Q are saying the same thing. But we cannot infer the truth of the statements. If both are knights, then both are telling the truth. However, if both are knaves then they are lying. Thus the identities of P and Q cannot be determined.