If F(A,B,C) =A',B',C' + A'.B.C' then find F' using De Morgan's Law.
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(AB’C + ABC’) (∵x’ + y’ = x’.y’)
= (AB’C’)’. (A’.B.C’)’ (∵(x’.y’) = x’ + y’) = ((A’B’)’ + (C)’. ((A’B)’ + (C’)’)
= ((A’)’ + (B’)’) + C).((A’)’ + (B)’ + C)
= (A + B + C).(A + B’ + C)
= AA + AB’ + AC + BA + BB’ + BC + CA + CB’ + CC (∵x.x = x)
= A + AB’ + C + AC + AB + B’C.
= (AB’C’)’. (A’.B.C’)’ (∵(x’.y’) = x’ + y’) = ((A’B’)’ + (C)’. ((A’B)’ + (C’)’)
= ((A’)’ + (B’)’) + C).((A’)’ + (B)’ + C)
= (A + B + C).(A + B’ + C)
= AA + AB’ + AC + BA + BB’ + BC + CA + CB’ + CC (∵x.x = x)
= A + AB’ + C + AC + AB + B’C.
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