All 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?
Options:
(A) Both P and Q are knights
(B) P is a knight; Q is a knave
(C) Both P and Q are knaves
(D) The identities of P, Q cannot be determined
Official Answer Key:
D
Step-by-Step Solution & Explanation
• Test P = knight: statement “both of us are knights” must be true ⇒ Q is also a knight. Check Q’s statement “none of us are knaves” — true, since both are knights, consistent with Q (a knight) telling the truth. This scenario (both knights) is self-consistent.
• Test P = knave: statement “both of us are knights” is false, so it is not the case that both are knights (automatically true since P is a knave) — consistent so far regardless of Q. If Q were a knight, Q’s statement “none of us are knaves” would have to be true, but P is a knave, so this would be false — contradiction, so Q cannot be a knight in this branch. If Q is a knave, Q’s statement must be false; “none of us are knaves” is indeed false because P is a knave — consistent. So (P knave, Q knave) is also self-consistent.
• Two distinct, fully self-consistent solutions exist — (both knights) and (both knaves) — so the identities cannot be uniquely pinned down from the statements alone.
• Final Answer: (D) The identities of P, Q cannot be determined
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.