Законы алгебры логики

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Документ описывает основные законы алгебры логики, включая законы двойного отрицания, исключённого третьего и непротиворечия. Включает переместительные, сочетательные, распределительные, поглощающие и другие свойства логических операций. Также представлены правила де Моргана и свойства констант.

Законы алгебры логики
1. Двойного отрицания:
¬¬A=A .
2. Исключённого третьего:
A∨¬A=1.
3. Непротиворечия:
A & ¬A=0 .
4. Переместительные:
● A & B=B & A ;
● A∨B=B∨A .
5. Сочетательные:
● A & B& C=A & B & C;
● A∨B∨C=A∨B∨C.
6. Распределительные:
● A &B∨C=A & B∨A & C ;
● A∨B & C=A∨B& A∨C.

7. Повторения:
● A & A=A ;
● A∨A=A .
8. Поглощения:
● A &A∨B=A ;
● A∨A & B=A .
9. Склеивания:
● A∨B&¬A∨B=B ;
● A & B∨¬A & B=B .
10. Свойства констант:
● A & 1=A , A & 0=0 ;
● A∨0=A , A∨1=1 .
11. Правила де Моргана:
● ¬ A & B=¬A∨¬B ;
● ¬ A∨B=¬A & ¬B .

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