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Задача
: Убедитесь, что доказательство для ( A \implies
eg A ) ведёт к AĆ неверно.
Доказательство
:
Пусть ( A \implies
eg A ).
Предположим ( A ) истинно. По предположению ( A \implies \A ). Это означает, что если ( A ) истинно, то (
eg A ) тоже должно быть истинно. Но это невозможно. Таким, как ( \A ) истинА. Таким образом, из предположения ( A ) следует противоречие. Следовательно, ( A ) ложно.
Таким образом, мы доказали, что ( A ) ложно. Но это не означает, что ( A ) истинно. На самом деле, мы доказали (
eg A ). Таким образом, ( A \implies
eg A ) не влечёт ( A ).
Объяснение
:
Доказательство в изображении показывает, что из ( A \implies
eg A ) можно вывести (
eg A ), но не ( A ). Таким образом, утверждение в изображении ошибочно.
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