Examples (cont’d)

• Prove the consensus theorem, which says:

  XY + X’Z + YZ = XY + X’Z
  

• Solution:

  XY + X’Z + YZ
  
  = XY + X’Z + (X + X’)YZ
  = XY + X’Z + XYZ + X’YZ
  = XY + XYZ + X’Z + X’ZY
  = XY(1 + Z) + X’Z(1 + Y)
  = XY + X’Z

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