Fundamentals of Boolean Algebra (8)

• Theorem 9 (Consensus)

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

• Examples:

  • AB + A'CD + BCD = AB + A'CD [T9(a)]
  • (a + b')(a' + c)(b' + c) = (a + b')(a' + c) [T9(b)]
  • ABC + A'D + B'D + CD = ABC + (A' + B')D + CD [P5(b)]
    = ABC + (AB)'D + CD [T8(b)]
    = ABC + (AB)'D [T9(a)]
    = ABC + (A' + B')D [T8(b)]
    = ABC + A'D + B'D [P5(b)]

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