Boolean Algebra

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

	Boolean Algebra
Kommutativ	\(x \cdot y = y \cdot x\)
	\(x + y = y + x\)
Assoziativ	\(x \cdot (y \cdot z) = (x \cdot y) \cdot z\)
	\(x + (y + z) = (x + y) + z\)
Distributiv	\(x \cdot (y + z) = x \cdot y + x \cdot z\)
	\(x + (y \cdot z) = (x + y) \cdot (x + z)\)
Indempotenz	\(x \cdot x = x\)
	\(x + x = x\)
Absorbtion	\(x \cdot (x+y) = x\)
	\(x + (x \cdot y) = x\)
Neutral	\(x \cdot 1 = x\)
	\(x + 0 = x\)
Dominant	\(x \cdot 0 = 0\)
	\(x + 1 = 1\)
Komplement	\(x \cdot \overline{x} = 0\)
	\(x + \overline{x} = 1\)
	\(\overline{\overline{x}} = x\)
De Morgan	\(\overline{x \cdot y} = \overline{x} + \overline{y}\)
	\(\overline{x + y} = \overline{x} \cdot \overline{y}\)