One of four suspects A, B, C and D has committed a crime. A and D are always truthful, and B and C are always untruthful. C and D are identical twins and the interrogator does not know who is who. If A says, "D is innocent", B says, "A is guilty" and among C and D one says, "A is innocent" and the other says, "B is guilty", then which of the following is FALSE?
This problem involves analyzing statements made by suspects with known truth-telling or lying tendencies to determine their guilt or innocence and identify which statement is false. We have four suspects: A, B, C, and D. A and D always tell the truth, while B and C always lie. C and D are identical twins, making it tricky to distinguish them initially.
Suspect Analysis and Statement Evaluation
Let's break down the information given:
- A: Truthful
- B: Untruthful (Liar)
- C: Untruthful (Liar)
- D: Truthful
C and D are twins, one truthful (D), one untruthful (C).
Evaluating Individual Statements
- A says, "D is innocent": Since A is always truthful, this statement is true. Therefore, D is innocent.
- B says, "A is guilty": Since B is always untruthful, this statement is false. The opposite must be true. Therefore, A is not guilty (A is innocent). This aligns with A being truthful, as a truthful person is unlikely to be the criminal.
- Among C and D, one says, "A is innocent" and the other says, "B is guilty":
- We know D is truthful and C is untruthful.
- We know "A is innocent" is a true statement (from evaluating A's and B's statements).
- Since D is truthful, D must be the one who says the true statement. Thus, D says, "A is innocent".
- This leaves C, the untruthful twin, to say the other statement: C says, "B is guilty".
- Since C is untruthful, C's statement "B is guilty" must be false. The opposite is true: B is not guilty (B is innocent).
Summary of Deductions
Based on the statements and the nature of the suspects, we can deduce the following:
- A is truthful and innocent.
- B is untruthful and innocent.
- D is truthful and innocent.
- C is untruthful. C said "B is guilty" which is a lie. If B is innocent (which we deduced), then C lied. This fits C's nature. Since only one suspect committed the crime, and A, B, and D are innocent, C must be the guilty one.
Let's summarise who is truthful/untruthful, who is innocent/guilty, and what each person said:
| Suspect | Truthful/Untruthful | Innocent/Guilty | Statement Made | Truth of Statement |
|---|---|---|---|---|
| A | Truthful | Innocent | "D is innocent" | True |
| B | Untruthful | Innocent | "A is guilty" | False |
| C (Twin) | Untruthful | Guilty | "B is guilty" | False |
| D (Twin) | Truthful | Innocent | "A is innocent" | True |
Evaluating the Options
We need to find the statement among the options that is FALSE based on our deductions.
- D said "A is innocent": From our analysis, D (the truthful twin) said "A is innocent". This statement is TRUE.
- D is innocent: From A's statement and our deductions, D is indeed innocent. This statement is TRUE.
- B is innocent: From C's lie ("B is guilty"), we deduced that B is innocent. This statement is TRUE.
- C is innocent: From our deductions, C is the untruthful twin who lied about B, and is the only remaining suspect who could have committed the crime. C is guilty, not innocent. This statement is FALSE.
Therefore, the statement that is FALSE is "C is innocent".
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