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Question

某公司被竊,A、B、C、D四人涉嫌被拘留。偵破結果顯示,罪犯就是其中的某一個人。 A說:「是C偷的。」B說:「我沒偷。」C說:「我也沒偷。」D說:「如果B沒有偷,那麼就是我偷的。」現已查明,其中只有一個人說了假話,從上述條件可以確定，誰偷成立?

Thought

分析各嫌疑人的陈述

我在分析A、B、C、D四人的陈述时，发现只有一个人说谎。A说C偷了，B和C否认偷窃，D说如果B未偷窃，则他偷了。

分析推测

我正在推测可能的偷窃者，并检查每种推测下的真假陈述，确保只有一个人说谎。

CHUNK: 根据D的说法，B没偷窃，所以他偷了。但假设A偷了，D的条件语句“如果B没偷窃，那么我偷了”是假的，因为他没偷（A偷了）。条件语句“如果P那么Q”只有在P为真且Q为假时为假。所以D在撒谎。但在这种情景下，A和D都是在说谎的，这种情景是无效的。

分析案件情况

我正在考虑B是否是小偷。通过检查每个人的陈述，我发现A和B都在撒谎。不可能只有一个人撒谎，所以这个情况无效。

推理过程

D说如果B没偷，那么我偷了，但D没偷，意味着前提是真的。D说如果B没偷，那么我偷了，但B没偷，所以结论是否定的。这个条件是假的，说明D在撒谎。由此可见，C和D都在撒谎。

Answer

Based on the given statements and the condition that only one person lied, let's determine who the thief is by evaluating each possible scenario.

Case 1: Assume A is the thief.

  • A's statement: "C stole." This is false since A is the thief. (Liar)
  • B's statement: "I didn't steal." True. (Truthful)
  • C's statement: "I didn't steal either." True. (Truthful)
  • D's statement: "If B didn't steal, then I stole." Since B didn't steal, D implies he is the thief, but A is the thief. This makes D's conditional statement false. (Liar)

This scenario has two liars (A and D), which contradicts the condition that only one person lied.

Case 2: Assume B is the thief.

  • A's statement: "C stole." False. (Liar)
  • B's statement: "I didn't steal." False since B is the thief. (Liar)
  • C's statement: "I didn't steal either." True. (Truthful)
  • D's statement: "If B didn't steal, then I stole." Since B did steal, the antecedent is false, making the whole conditional statement vacuously true. (Truthful)

This scenario has two liars (A and B), violating the one-lie condition.

Case 3: Assume C is the thief.

  • A's statement: "C stole." True. (Truthful)
  • B's statement: "I didn't steal." True. (Truthful)
  • C's statement: "I didn't steal either." False. (Liar)
  • D's statement: "If B didn't steal, then I stole." Since B didn't steal and D didn't steal, the conditional statement is false. (Liar)

This scenario has two liars (C and D), which is invalid.

Case 4: Assume D is the thief.

  • A's statement: "C stole." False. (Liar)
  • B's statement: "I didn't steal." True. (Truthful)
  • C's statement: "I didn't steal either." True. (Truthful)
  • D's statement: "If B didn't steal, then I stole." B didn't steal, and D did steal, making the conditional statement true. (Truthful)

In this case, only A is lying, satisfying the condition that only one person lied.

Conclusion: D is the thief.

Answer: D

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