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