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Definition

The boolean algebra (0,1;,+,x¯)({0,1};\cdot , +, \overline{x})

Boolean Algebra
Kommutativ xy=yxx \cdot y = y \cdot x
x+y=y+xx + y = y + x
Assoziativ x(yz)=(xy)zx \cdot (y \cdot z) = (x \cdot y) \cdot z
x+(y+z)=(x+y)+zx + (y + z) = (x + y) + z
Distributiv x(y+z)=xy+xzx \cdot (y + z) = x \cdot y + x \cdot z
x+(yz)=(x+y)(x+z)x + (y \cdot z) = (x + y) \cdot (x + z)
Indempotenz xx=xx \cdot x = x
x+x=xx + x = x
Absorbtion x(x+y)=xx \cdot (x+y) = x
x+(xy)=xx + (x \cdot y) = x
Neutral x1=xx \cdot 1 = x
x+0=xx + 0 = x
Dominant x0=0x \cdot 0 = 0
x+1=1x + 1 = 1
Komplement xx¯=0x \cdot \overline{x} = 0
x+x¯=1x + \overline{x} = 1
x¯¯=x\overline{\overline{x}} = x
De Morgan xy¯=x¯+y¯\overline{x \cdot y} = \overline{x} + \overline{y}
x+y¯=x¯y¯\overline{x + y} = \overline{x} \cdot \overline{y}