Question

На вопрос, кто из А, В, С, D, Е играет в шахматы, получено пять ответов. 1) Если А играет, то и В играет. 2) D и Е или играют оба, или играет только один из них. 3) Из В и С играет только один. 4) С и D или оба играют, или оба не играют. 5) Если Е играет, то и А и D тоже играют. Кто из пятерых играет в шахматы?

Answer 1

Предположим, что E играет, тогда, исходя из (д) , A и D играют.
Из (а) следует, что B играет.
Из (в) следует, что C не играет.
Приходим к противоречию (см. г) , т. к. C не играет, а D играет.

Следовательно, E не играет.
Из (б) следует, что D играет.
Из (г) следует, что C играет.
Из (в) следует, что B не играет.
Из (а) следует, что A не играет.

Answer 2

Who plays chess among A, B, C, D, and E?

To determine who plays chess among A, B, C, D, and E, we can analyze the given statements:

1) If A plays, then B plays. 2) Either D and E both play or only one of them plays. 3) Only one of B and C plays. 4) Either both C and D play or neither of them plays. 5) If E plays, then both A and D also play.

Let's break down the statements and analyze them one by one:

Statement 1: If A plays, then B plays. This means that if A plays chess, then B also plays chess.

Statement 2: Either D and E both play or only one of them plays. This statement implies that either both D and E play chess or only one of them plays chess.

Statement 3: Only one of B and C plays. This statement indicates that only one of B and C plays chess.

Statement 4: Either both C and D play or neither of them plays. According to this statement, either both C and D play chess or neither of them plays chess.

Statement 5: If E plays, then both A and D also play. This statement suggests that if E plays chess, then both A and D also play chess.

Based on these statements, we can deduce the following:

- If A plays chess, then B also plays chess (Statement 1). - If E plays chess, then both A and D also play chess (Statement 5). - Only one of B and C plays chess (Statement 3). - Either both C and D play chess or neither of them plays chess (Statement 4). - Either both D and E play chess or only one of them plays chess (Statement 2).

From these deductions, we can conclude that: - A plays chess. - B plays chess (since A plays chess, according to Statement 1). - C does not play chess (since only one of B and C plays chess, according to Statement 3). - D plays chess (since either both C and D play chess or neither of them plays chess, and C does not play chess, according to Statement 4). - E does not play chess (since either both D and E play chess or only one of them plays chess, and D plays chess, according to Statement 2).

Therefore, among A, B, C, D, and E, A, B, and D play chess.

Please let me know if you need any further clarification or assistance!