Question

Expand the following expression using De Morgan's theorem.

F2(A,B,C) = ((AB + B'C).(AC + A'C'))'

Answer 1

F2(A,B,C) = ((AB + B′C)(AC + A′C′))′

Using De Morgan's theorem:

F2 = (AB + B′C)′ + (AC + A′C′)′

= [(AB)′(B′C)′] + [(AC)′(A′C′)′]

= (A′+B′)(B + C′) + (A′ + C′)(A + C)

Therefore,

F2 = (A′ + B′)(B + C′) + (A′ + C′)(A + C)

On simplification:

F2 = A′ + C′