S-o-P, P-o-S, and de Morgan’s theorem

• Sum-of-products

  • F' = A'B'C' + A'BC' + AB'C'

• Apply de Morgan's

  • (F')' = (A'B'C' + A'BC' + AB'C')'
  • F = (A + B + C) (A + B' + C) (A' + B + C)

• Product-of-sums

  • F' = (A + B + C') (A + B' + C') (A' + B + C') (A' + B' + C) (A' + B' + C')

• Apply de Morgan's

  • (F')' = ( (A + B + C')(A + B' + C')(A' + B + C')(A' + B' + C)(A' + B' + C') )'
  • F = A'B'C + A'BC + AB'C + ABC' + ABC

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