Boolean Expression minimization

Question

Can someone help confirm that I simplified correctly?

$F=(\neg ( A * \neg B) * (B * \neg C) * \neg B ) + D$

For my answer, I get:

$F = A*\neg B*C+D$

Answer 1

Hint:

Your answer is not correct, it simplify to $D$, just notice that the first term: $$(\neg ( A * \neg B) * (B * \neg C) * \neg B )$$ is a contradiction, since $B$ and $\neg B$ can never hold at the same time.

Answer: (Use Laws of Boolean algebra)

\begin{align}&(\neg ( A * \neg B) * (B * \neg C) * \neg B ) + D\\=&(\neg ( A * \neg B) * (\neg C * B) * \neg B ) + D\tag*{Commutativity}\\=&(\neg ( A * \neg B) * \neg C * (B * \neg B) ) + D\tag*{Associativity}\\=&(\neg ( A * \neg B) * \neg C * (0) ) + D\tag*{Complementation}\\=&~0 + D\tag*{Annihilator}\\=&~D\tag*{Identity}\\\end{align}