12. Given that F = (A + B'+ C)(D + E), which of the following represents the only correct expression for F'?

  1. F' = A'BC'+ D'+ E'
  2. F' = AB'C + DE
  3. F' = (A'+ B + C')(D'+ E')
  4. F' = A'BC' + D'E'
  5. F' = (A + B'+ C)(D'+ E')

4 is CORRECT. 

F' = ((A + B'+ C) * (D + E))' 
   =  (A + B'+ C)'+ (D + E)'  by Demorgan's law
   =   A'* B * C' +  D'* E'   by Demorgan's law again

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