Logic Problem: Knight vs. Knave

Logic Problems: Knight and Knave

• The problem of the Knight and Knave is a classic logic problem where two individuals, one who always tells the truth (Knight) and one who always lies (Knave), are encountered on a path.
• The first person says "we are both Knaves", and the goal is to determine who is the Knight and who is the Knave.

Truth Tables

• Truth tables are used to perform logical operations between inputs to show a final output.
• They determine the truth value of an argument.
• In the case of the Knight and Knave problem, a truth table is used to examine all possible outcomes of the 1st and 2nd person lying or telling the truth.

Solving the Knight and Knave Problem

• If the first person is telling the truth, it would make both the 1st and 2nd person Knaves, regardless of whether the second person is telling the truth or not.
• If the first person is lying, they can't be a Knight, but because their statement is a lie, it would make the 2nd person a Knight.
• By looking at the truth tables, we can conclude that the 1st person is the Knave and the 2nd person is the Knight.

Common Logic Operations

• AND (Λ) is a logic operation where both inputs need to be true for the output to be true.
• OR (v) is a logic operation where only one or the other input needs to be true for the output to be true.
• NOT (~) is a logic operation for negation where the opposite of the input is the result.

Truth Tables for Logic Operations

• AND (Λ) truth table:
  • T T → T
  • T F → F
  • F T → F
  • F F → F
• OR (v) truth table:
  • T T → T
  • T F → T
  • F T → T
  • F F → F
• NOT (~) truth table:
  • T → F
  • F → T

Solve the classic logic problem of the Knight and Knave, a brain teaser that has inspired many other logical puzzles. Learn to think critically and make the right choice.