Polsl-Notes/TC/Ściągi/ALGEBRA BOOLOWSKA.md

Aksjomaty algebry boola

1. (\bar 0 = 1) \cap (\bar 1 = 0)
2. (x+1=1) \cap (x \cdot 1 = x) - 1 elementem neutralnym dla iloczynu
3. (x+0=x) \cap (x \cdot 0 = 0) - 0 elementem neutralnym dla sumy
4. (x + \bar x = 1) \cap (x \cdot \bar x = 0) - Prawo negacji
5. (x+x=x)\cap (x\cdot x = x) - Prawo idempotentności
6. \bar{\bar x} = x
7. (\overline{x+y}=\bar{x}\cdot \bar{y})\cap (\overline{xy}=\bar{x}+\bar{y}) - Prawo de morgana - \overline{\bar{a}\cdot\bar{b}}=a+b
8. (x+y = y+x) \cap (x\cdot y = y \cdot x) - Prawo przemienności iloczynu/sumy
9. x+(y+z)=(x+y)+z\cap x(yz)=(xy)z
10. x(y+z)=xy+xz\cap x+(yz)=x+y \cdot x+z - Rozdzielność iloczynu względem sumy

Prawa Pochłaniania

1. x+xy=x \cap x(x+y)=x
2. \forall x,y \in B [x+\bar x y = x+y]\cap[x(\bar x+y)=xy]

Prawo Wklejania

1. (yx+\bar x=y)\cap[(y+x)(y+\bar x)=y]

%%za a+a=a^2 ban na życie%%

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