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See attachment:booleanalgebra.pdf / attachment:booleanalgebra.tex for complete pdf description.
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   x + (y * z) = (x + y) * (x + z)
   x + x' = 1
   x + 0 = x
   0 <> 1
   x * y = y * x
   x * (y + z) = (x * y) + (x * z)
   x * x' = 0
   x * 1 = x
   x * x = x		    Distributive + over * : x + (y * z) = (x + y) * (x + z)
   Addition of Complement : x + x' = 1
   Additive Identity : x + 0 = x
                           : 0 <> 1
   Commutivitity : x * y = y * x
   Distributive * over + : x * (y + z) = (x * y) + (x * z)
                           : x * x' = 0
   Multiplicative Identity : x * 1 = x
                           : x * x = x
Line 26: Line 28:
   * FreeBooleanAlgebra
   * PresburgerArithmetic

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See attachment:booleanalgebra.pdf / attachment:booleanalgebra.tex for complete pdf description.

A Boolean algebra B is a sextuple

  • <Domain, * (AND), + (OR), ' (complement), 0, 1>

The following rules hold for a boolean algebra: 

   Distributive + over *   : x + (y * z) = (x + y) * (x + z)
   Addition of Complement  : x + x' = 1
   Additive Identity       : x + 0 = x
                           : 0 <> 1
   Commutivitity           : x * y = y * x
   Distributive * over +   : x * (y + z) = (x * y) + (x * z)
                           : x * x' = 0
   Multiplicative Identity : x * 1 = x
                           : x * x = x

SEE ALSO:

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BooleanAlgebra (last edited 2005-06-16 14:57:52 by yakko)