Boolean algebra

• General rules for Boolean expressions

  • X^0=0
  • X^ 1 = X
  • XxX = X
  • X^ ¬X = 0
  • Xv0 = X
  • Xv1 = 1
  • XvX = X
  • Xv -X = 1
• Commutative rule

  • X^Y = Y^X
  • XvY = YvX
• Associative rules


  1. X^ (Y^Z) = (X^Y) ^ Z

  2. Xv (Yv Z) = (X v Y) v Z
• Distributive rules

  1. X^(YvZ) = (X^Y) V (X^Z)

  2. (XvY)^ (WvZ) = (X^ W) v (X^Z) v(Y^W)v (Y^Z)
• Absorption rules

  1. Xv (X^Y) = X

  2. X ^(XvY) = X
• Double negation

  X=~~X