Bolean algebra De morgan's law - can i use it from the outside to the inside like I did?

Question

I thought maybe the problem is because I used the morgan from the outside , I tried figuring out the problem for an hour and solved it like three times. I found some mistakes but thats the finale answer- and its not right.... why is it, does the morgan law has problems here in the way i did it ? How I tried to slove the problem

solution of my teacher

what is the problem with my solution?

$ABCD+\overline{\overline{A}*\overline{C}+A*\overline{B}+\overline{B*\overline{C}}}$

$ABCD+(A'C'+((AB')')*(B*C'))'$

$=ABCD+(A'C')'*(A*B')+B*C'+(B*C')'$

$ABCD+(A+C)*(A*B')+(B*C')'$

$ABCD+AB'+AB'C+\overline{BC'}$

$ABCD+AB'(1+C)+\overline{B*C'}$

$A(BCD+B')+B'+C=A(B'+CD)+B'+C=AB'+ACD+B'+C =B'(A+1)+C(AD+1)=B'+C$

Answer 1

what is the problem with my solution?

The very start.

$ABCD+\overline{\overline{A}*\overline{C}+A*\overline{B}+\overline{B*\overline{C}}}$

$ABCD+(A'C'+((AB')')*(B*C'))'$

It should be: $ABCD+{({A'}{C'}+A\cdot{B'}+{(B\cdot{C'})'})'}$