Project ForgeAll people in a certain island 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?
- ABoth P and Q are knights
- BP is a knight; Q is a knave
- CBoth P and Q are knaves
- The identities of P, Q cannot be determined
Explanation
Test self-consistency: if P is a knight, P's statement 'both of us are knights' must be true, so Q is also a knight, and Q's truthful statement 'none of us are knaves' is consistent (both knights) — this scenario works. Separately, if P is a knave, P's statement is false, meaning NOT both are knights; testing Q as also a knave: Q's lie 'none of us are knaves' is indeed false (both really are knaves) — consistent with Q lying too — this scenario ALSO works. Since two different, fully self-consistent identity assignments both satisfy the statements, the identities cannot be uniquely determined.
Source: GATE ME 2017 Session 2 (ME-2) (2017)
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