If F(A, B, C) = A’.B’.C’ + A’.B.C’ then find F’ using De M

1.	If F(A, B, C) = A’.B’.C’ + A’.B.C’ then find F’ using De Morgan’s Law.
Answer» (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 + BC

If F(A, B, C) = A’.B’.C’ + A’.B.C’ then find F’ using De Morgan’s Law.

Answer»

(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 + BC