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Консультация № 173180
11.10.2009, 19:12
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Доброго времени суток!
Данное суждение записать в виде формулы предикатов. Построить отрицание данного суждения в виде формулы, не содержащих внешних знаков отрицания. Перевести на естественный язык.
"Некоторые пассажиры не платят за проезд"
Данное суждение записать в виде формулы предикатов. Построить отрицание данного суждения в виде формулы, не содержащих внешних знаков отрицания. Перевести на естественный язык.
"Некоторые пассажиры не платят за проезд"
Обсуждение
12.10.2009, 19:19
общий
это ответ
Здравствуйте, Dflame.
Пусть на множестве всех пассажиров задан предикат P(x): «пассажир x платит за проезд». Тогда заданное суждение означает, что существует хотя бы один пассажир, который не платит за проезд. В виде формулы логики предикатов это суждение запишется так:
([$8707$]x)¬P(x),
а отрицание данного суждения – так:
¬(([$8707$]x)¬P(x)).
Перенося квантор существования через отрицание, в соответствии с правилами перехода от одних формул к им равносильным, получим искомую форму записи:
([$8704$]x)P(x),
что означает «все пассажиры платят за проезд».
С уважением.
Пусть на множестве всех пассажиров задан предикат P(x): «пассажир x платит за проезд». Тогда заданное суждение означает, что существует хотя бы один пассажир, который не платит за проезд. В виде формулы логики предикатов это суждение запишется так:
([$8707$]x)¬P(x),
а отрицание данного суждения – так:
¬(([$8707$]x)¬P(x)).
Перенося квантор существования через отрицание, в соответствии с правилами перехода от одних формул к им равносильным, получим искомую форму записи:
([$8704$]x)P(x),
что означает «все пассажиры платят за проезд».
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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