Fundamentals of Boolean Algebra (1)

• Basic Postulates

• Postulate 1 (Definition): A Boolean algebra is a closed algebraic system containing a set K of two or more elements and the two operators · and +.

• Postulate 2 (Existence of 1 and 0 element):

(a) a + 0 = a (identity for +), (b) a · 1 = a (identity for ·)

• Postulate 3 (Commutativity):

(a) a + b = b + a, (b) a · b = b · a

• Postulate 4 (Associativity):

(a) a + (b + c) = (a + b) + c (b) a· (b·c) = (a·b) ·c

• Postulate 5 (Distributivity):

(a) a + (b·c) = (a + b) ·(a + c) (b) a· (b + c) = a·b + a·c

• Postulate 6 (Existence of complement):

  (a) (b)
  

• Normally · is omitted.

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