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Консультация № 194582
03.02.2019, 20:57
0.00 руб.
03.02.2019, 22:50
1
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:Как доказать выражение в прямом и обратном порядке? выражение следующее: [$172$]((X[$8594$]Y)[$8744$]([$172$]Y[$8594$]Z))[$8801$]((X&[$172$]Y)&[$172$]Z) или можно посмотреть в прикрепленном файле.
Прикрепленные файлы:
Обсуждение
06.02.2019, 21:01
общий
это ответ
Здравствуйте, svitalij1983!
Доказательство в прямом порядке можно выполнить так:
В результате тождественных преобразований из левой части выражения получена правая часть.
Доказательство в обратном порядке можно выполнить, применив указанные преобразования "снизу вверх".
Доказательство в прямом порядке можно выполнить так:
[$172$]((X[$8594$]Y)[$8744$]([$172$]Y[$8594$]Z))[$8801$]
(по закону де Моргана)
[$8801$](X[$8594$]Y)[$8743$]([$172$]([$172$]Y[$8594$]Z))[$8801$]
(замена импликации дизъюнкцией)
[$8801$]([$172$]([$172$]VY))[$8743$]([$172$]([$172$][$172$]Y[$8744$]Z))[$8801$]
(по закону двойного отрицания)
[$8801$]([$172$]([$172$]X[$8744$]Y))[$8743$]([$172$](Y[$8744$]Z))[$8801$]
(по закону де Моргана)
([$172$]X[$8744$][$172$]Y)[$8743$]([$172$]Y[$8744$][$172$]Z)[$8801$]
(по закону двойного отрицания)
[$8801$](X[$8743$][$172$]Y)[$8743$]([$172$]Y[$8743$][$172$]Z)[$8801$]
(по закону ассоциативности конъюнкции)
[$8801$]X[$8743$][$172$]Y[$8743$][$172$]Y[$8743$][$172$]Z[$8801$]
(по закону идемпотентности конъюнкции)
[$8801$]X[$8743$][$172$]Y[$8743$][$172$]Z[$8801$]
(по закону ассоциативности конъюнкции)
[$8801$](X[$8743$][$172$]Y)[$8743$][$172$]Z.
В результате тождественных преобразований из левой части выражения получена правая часть.
Доказательство в обратном порядке можно выполнить, применив указанные преобразования "снизу вверх".
5
Отлично справились!!!!
Об авторе:
Facta loquuntur.
Facta loquuntur.
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