Fundamentals of Boolean Algebra (3)

• Theorem 4 (Absorption)

(a) a + ab = a (b) a(a + b) = a

• Examples:

  • (X + Y) + (X + Y)Z = X + Y [T4(a)]
  • AB'(AB' + B'C) = AB' [T4(b)]
    

• Theorem 5

(a) a + a'b = a + b (b) a(a' + b) = ab

• Examples:

  • B + AB'C'D = B + AC'D [T5(a)]
  • (X + Y)((X + Y)' + Z) = (X + Y)Z [T5(b)]

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