Question

Серёга и Коля гостили летом у бабушки. Однажды один из мальчиков нечаяно разбил любимую бабушкину вазу. На вопрос, кто разбил вазу, оди дали такие ответы. Серёжа: 1) Я не разбивал. 2) Вася не разбивал. Вася: 3) Серёжа не разбивал. 4) Вазу разбил Коля. Коля: 5) Я не разбивал. 6) Вазу разбил Серёжа. Бабушка знала, что один из её внуков (правдивый), оба раза сказал правду; второй (шутник) оба раза сказал неправду; третий (хитрец) один раз сказал правду, а другой раз неправду. Назовите имяна правдивого шутника и хитреца. Кто из внуков разбил вазу? Вычислите это через таблицу истинности.

Answer 1

Ответ:

Чашку разбил Серёжа. Коля – правдивый, Серёжа – хитрец, Вася – шутник

Объяснение:

Answer 2

To solve this problem, we can create a truth table to analyze the statements made by each person and determine who broke the vase. Let's assign variables to represent the statements:

- S: Serёga broke the vase - K: Kolya broke the vase

Based on the given information, we can construct the truth table:

| Statement | S | K | |-----------|---|---| | 1 | 0 | 0 | | 2 | 0 | 0 | | 3 | 0 | 0 | | 4 | 1 | 0 | | 5 | 0 | 0 | | 6 | 1 | 0 |

Now, let's analyze each statement:

1. Serёga says, "I didn't break it." This means S is false (0). 2. Vasya says, "I didn't break it." This means K is false (0). 3. Serёga says, "Vasya didn't break it." This means S is false (0). 4. Kolya says, "I broke the vase." This means K is true (1). 5. Kolya says, "I didn't break it." This contradicts statement 4, so K is false (0). 6. Kolya says, "Serёga broke the vase." This contradicts statement 4, so K is false (0).

Based on the truth table, we can see that statement 4 is the only one consistent with the given information. Therefore, Kolya is the one who broke the vase.

As for the truthful person and the joker, we can analyze the statements:

- The truthful person always tells the truth. - The joker always lies.

From the truth table, we can see that statement 4 is true, which means Kolya broke the vase. This means that the truthful person is Kolya.

Since the joker always lies, the joker is Serёga.

To summarize: - The truthful person is Kolya. - The joker is Serёga. - Kolya broke the vase.

Please let me know if there is anything else I can help you with!