Spies and Double Agents

number of statements

4

5

new puzzle

show solution

solution

truth tables of trustworthy

truth tables of untrustworthy

M's statements

D ⇔ (¬C ∨ ¬B)

¬C ∨ (¬D ∧ A)

D ∧ (¬A ⇔ ¬B)

¬A ∧ (¬B  C)

N's statements

B ∧ (D ∨ ¬C)

¬C  (D ∨ ¬A)

B ∨ (D ∧ ¬A)

¬B ⇔ (¬A ∨ ¬C)

Who is trustworthy and what are truth values of the statements?

Two logical spies, M and N, sent reports to Z, the head of the CIA. Z suspected one to be a double agent. The task is to find which spy is trustworthy and always tells the truth, which spy is untrustworthy and always lies, and to evaluate their statements,

A

,

B

,

C

, …, for their truth values. The contents of the statements are classified. For negation, conjunction, disjunction, implication, and equivalence, they used the symbols

¬

,

∧

,

∨

,



,

⇔

. For readability, F (for False) is left blank in the truth tables.