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Здравствуйте! Прошу помощи в следующем вопросе: Решить задачу с помощью поиска минимальной КНФ. Семья решила купить новый шкаф. Все хотели, чтобы шкаф был либо дубовый, либо березовый; либо желтый, либо коричневый; либо светлый, либо темный. Отцу дали рекомендации: 2.1. Ты можешь купить светлый шкаф, если только он будет березовым желтого цвета. 2.2. Если шкаф будет березовым, то светлый тон должен быть достаточным признаком желтой окраски. 2.3. Если шкаф будет коричневым, то для того, чтобы он был темным, необходимо, чтобы он был сделан из дуба. Все эти условия можно свести к двум простейшим. Отцом был куплен шкаф, который удовлетворял только одному из этих условий. Он поступил так, потому что хотел, чтобы шкаф был светлым и березовым или темным, но желтым. И это условие действительно оказалось выполненным. Какой шкаф был куплен?
x - дубовый, -x - березовый y - желтый, -y - коричневый z - светлый, -z - темный
1) z->-xy -z [$8744$] -xy Шкаф или темный, или березовый желтого цвета 2) -x->(z->y) x[$8744$]-z[$8744$]y шкаф дубовый или желтый или темный 3) -y->(-z->x) y[$8744$]z[$8744$]x Шкаф дубовый или желтый или светлый
2 и 3 условие являются конъюнктами. 1 можно привести к КНФ -z[$8744$]-x [$8743$]-z[$8744$]y=-x[$8744$]y[$8744$]-z [$8743$]-x[$8744$]-y[$8744$]-z [$8743$]x[$8744$]y[$8744$]-z Условие 2 уже содержится в этом КНФ Соединяя с 3, получим -x[$8744$]y[$8744$]-z [$8743$]-x[$8744$]-y[$8744$]-z [$8744$]x[$8744$]y[$8744$]-z [$8743$]x[$8744$]y[$8744$]z=-x[$8744$]-z[$8743$]x[$8744$]y Простейшие условия - шкаф березовый или темный и дубовый или желтый Условие папы -xz[$8744$] y-z И всем условиям удовлетворяют 3 вида шкафов 1 шкаф был дубовый желтый темный. 2 березовый желтый темный 3 березовый желтый светлый
Форма ответа
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