vault backup: 2023-03-01 10:15:26

TC/ALGEBRA BOOLE'a.md

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+# Aksjomaty algebry boola
+1. $(\bar 0 = 1) \cap (\bar 1 = 0)$
+2. $\forall x\in B  (x+1=1) \cap (x \cdot 1 = x)$
+3. $\forall x\in B  (x+0=x) \cap (x \cdot 0 = 0)$
+4. $(x + \bar x = 1) \cap (x \cdot \bar x = 0)$
+5. $(x+x=x)\cap (x\cdot x = x)$
+6. $\bar{\bar x} = x$ 
+7. $\forall x,y \in B\ \ (\overline{x+y}=\bar{x}\cdot \bar{y})\cap (\overline{xy}=\bar{x}+\bar{y})$  prawo de morgana
+8. $(x+y = y+x) \cap (x\cdot y = y \cdot x)$
+9. $x+(y+z)=(x+y)+z\cap x(yz)=(xy)z$
+10. $x(y+z)=xy+xz\cap x+(yz)=x+y \cdot x+z$
+
+# 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. $(yx+\bar x=y)\cap[(y+x)(y+\bar x)=y]$