_ _ _ _ _ _ _ _ _ _ _ _ F = (A + D)*(B + C) = A*B + A*C + B*D + C*DOr we can look at the pulldown circuitry and express F as the complement of the function that describes when the pulldown is on:
_________ F = A*D + B*CUsing several applications of DeMorgan's theorem this can be expanded to
___ ___ _ _ _ _ F = (A*D)*(B*C) = (A + D)*(B + C)which is the expression we derived using the pullup circuitry.
_________ ___ _ _ _ _ _ _ _ _ F = (A*B) + C = (A*B)*C = (A + B)*C = A*C + B*C