Simplification of the expression using De-Morgan's rule

Question

Simplify the following expressions to the simplest expression using De Morgan’s theorem and Boolean algebra.

¬(A(¬(B+¬C))D)=¬(AD(¬(B+¬C))

          =¬(AD)+¬(¬(B+¬C))
          =¬(AD)+(B+¬C)
          =¬(AD)+B+¬C 

is the solution correct?

Many thanks!

Answer 1

I am reading this as:

$\neg (A \land \neg (B \lor \neg C) \land D)$

which by DeMorgan would be:

$\neg A \lor (B \lor \neg C) \lor \neg D$

i.e.

$\neg A + B + \neg C + \neg D$