Diff for "BooleanAlgebra"

Differences between revisions 2 and 9 (spanning 7 versions)

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

-  ⇤ ← Revision 2 as of 2003-11-04 00:45:41 → 
  Size: 362
  Editor: wakko
  Comment:
+   ← Revision 9 as of 2005-06-16 14:57:52 → ⇥
  Size: 846
  Editor: yakko
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
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+See attachment:booleanalgebra.pdf / attachment:booleanalgebra.tex for complete pdf description.
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+Line 9:
-Essentially this is an algebra such that a*a = a.
+The following rules hold for a boolean algebra:
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+Line 12:
-   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
+   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 18:
+Line 22:
+SEE ALSO:

   * BooleanTerm
   * GroundBooleanTerm
   * MonotoneBooleanTerm
   * FreeBooleanAlgebra
   * PresburgerArithmetic