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Консультация № 195444
01.05.2019, 17:44
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Найти множество истинности двуместных предикатов:
а) x>1 v y<1;
b) x>1 [$8596$] y<1
Найти множество истинности двуместных предикатов:
а) x>1 v y<1;
b) x>1 [$8596$] y<1
Обсуждение
03.05.2019, 12:02
общий
это ответ
Здравствуйте, Smurf!
Пусть оба предиката определены на множестве всех вещественных чисел.
а) Заданная дизъюнкция истинна, если x>1 или y<1, или одновременно x>1 и y<1. Поэтому искомое множество истинности образовано парами действительных чисел, которые являются координатами точек плоскости, расположенных или ниже прямой y=1 (независимо от x), или правее прямой x=1 (независимо от y). На рисунке ниже эта область закрашена. Граница, обозначенная штрихами, этому множеству не принадлежит.
б) Поскольку (A[$8596$]B)[$8801$](A[$8594$]B)[$8743$](B[$8594$]A)[$8801$]([$172$]A[$8744$]B)[$8743$](A[$8744$][$172$]B), постольку (x>1[$8596$]y<1)[$8801$](x[$8804$]1[$8744$]y<1)[$8743$](x>1[$8744$]y[$8804$]1). Множество истинности первого члена конъюнкции показано на рисунке слева, множество истинности второго члена конъюнкции -- на рисунке справа.
Искомое множество истинности заданной эквиваленции является пересечением этих двух множеств. Оно показано на рисунке ниже.
Пусть оба предиката определены на множестве всех вещественных чисел.
а) Заданная дизъюнкция истинна, если x>1 или y<1, или одновременно x>1 и y<1. Поэтому искомое множество истинности образовано парами действительных чисел, которые являются координатами точек плоскости, расположенных или ниже прямой y=1 (независимо от x), или правее прямой x=1 (независимо от y). На рисунке ниже эта область закрашена. Граница, обозначенная штрихами, этому множеству не принадлежит.
б) Поскольку (A[$8596$]B)[$8801$](A[$8594$]B)[$8743$](B[$8594$]A)[$8801$]([$172$]A[$8744$]B)[$8743$](A[$8744$][$172$]B), постольку (x>1[$8596$]y<1)[$8801$](x[$8804$]1[$8744$]y<1)[$8743$](x>1[$8744$]y[$8804$]1). Множество истинности первого члена конъюнкции показано на рисунке слева, множество истинности второго члена конъюнкции -- на рисунке справа.
Искомое множество истинности заданной эквиваленции является пересечением этих двух множеств. Оно показано на рисунке ниже.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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