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GATE 2017 ME (ME2) – Question 9

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 2 marks · Multiple choice

Everyone on an island is either a knight, who never lies, or a knave, who always lies; everyone knows everyone else’s identity. P says “Both of us are knights.” Q says “None of us are knaves.” What follows?

  1. Both P and Q are knights
  2. P is a knight; Q is a knave
  3. Both P and Q are knaves
  4. Their identities cannot be determined

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Show answer and explanation

Correct answer: (D) Their identities cannot be determined

Explanation

Both statements assert that both people are knights. If both are knights, both statements are true and consistent. If both are knaves, both statements are false and also consistent. A mixed pair would make the knight speak falsely. Since two assignments remain possible, the identities **cannot be determined, D**.