I need to simplify the following logic expression:
$$\begin{array}{|c|c|c|c|c|}
\hline
A & B & C & X & SOP \\
\hline
0 & 0 & 0 & 0 & \\
\hline
0 & 0 & 1 & 1 & \overline{A}\ \overline{B}C \\
\hline
0 & 1 & 0 & 1 & \overline AB\overline C\\
\hline
0 & 1 & 1 & 1 & \overline ABC \\
\hline
1 & 0 & 0 & 0 & \\
\hline
1 & 0 & 1 & 1 & A\overline BC\\
\hline
1 & 1 & 0 & 0 &\\
\hline
1 & 1 & 1 & 1 & ABC \\
\hline
\end{array}$$
$$X=\overline{A}\ \overline{B}C+\overline AB\overline C+\overline ABC+A\overline BC+ABC$$
I get the following logic expression after simplification:
$$\begin{aligned}X
&=\overline{A}\ \overline{B}C+\overline AB\overline C+\overline ABC+A\overline BC+ABC\\
&=ABC+\overline ABC+\overline{A}\ \overline{B}C+A\overline BC+\overline AB\overline C\\
&=BC(A+\overline A)+\overline BC(A+\overline A)+\overline AB\overline C\\
&=BC+\overline BC+\overline AB\overline C\\
&=C(B+\overline B)+\overline AB\overline C\\
&=C+\overline AB\overline C
\end{aligned}$$
However, K-MAP and Logic Friday each give me a different answer.
Edit: I changed the SOP, there was a mistake.
Best Answer
The point where you arrived is almost right:
$$ C+\overline{A}B\overline{C}=C(1+\overline{A}B)+\overline{A}B\overline{C}=\\= C+\overline{A}BC+\overline{A}B\overline{C}=C+\overline{A}B(C+\overline{C})=\\= C+\overline{A}B $$
That should be the same answer the K-map and whatever reduction software should give you.