Analyze Knights-and-Knaves Dialogue Variants

Q: Analyze Knights-and-Knaves Dialogue Variants

This question evaluates proficiency in formal logical reasoning, truth-functional analysis, and consistency checking within constrained dialogue puzzles (knights-and-knaves), focusing on identifying consistent truth assignments.

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Question

Knights and Knaves: Two Statements from B

Context

On an island, every person is either a knight (always tells the truth) or a knave (always lies). You meet two people, A and B. Person B makes two statements:

First, B says to A: "You always lie." (i.e., B asserts that A is a knave.)
Then B makes exactly one of the following additional claims:
1. "A is a knave and B is a knight."
2. "A is a knight and B is a knave."
3. "A is a knave and B is a knave."
4. "A is a knight and B is a knight."

Task

For each variant (1–4) independently, determine the logically consistent identities of A and B (knight or knave), or conclude that the information is insufficient or inconsistent. Show your reasoning.

Analyze Knights-and-Knaves Dialogue Variants

Knights and Knaves: Two Statements from B

Context

Task

Solution

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Analyze Knights-and-Knaves Dialogue Variants

Overview

Knights and Knaves: Two Statements from B

Context

Task

Solution

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