<s>[INST] Boolean Algebra simplify minterms I have this equation 
$$\bar{A}\cdot\bar{B}\cdot\bar{C} + A\cdot\bar{B}\cdot C + A\cdot B\cdot \bar{C} + A \cdot B\cdot C$$
and need to simplify it. I have got as far as I can and spent a good 2 hours at it. I've realized I now need to use De Morgan's law to continue however I am baffled as to which rule to use. If someone could send me in the right direction that would be great!
$$\bar{A}\cdot\bar{B}\cdot\bar{C} + A\cdot\bar{B}\cdot C + A\cdot B\cdot \bar{C} + A \cdot B\cdot C$$
$$\bar{A}\cdot\bar{B}\cdot\bar{C} + A(\bar{B}\cdot\bar{C} + B\cdot\bar{C} + B\cdot C$$
$$\bar{A}\cdot\bar{B}\cdot\bar{C} + A(\bar{B}\cdot C + B(\bar{C} + C)) $$
$$\bar{A}\cdot\bar{B}\cdot\bar{C} + A(\bar{B}\cdot C + B) $$ 
$$\bar{A}\cdot\bar{B}\cdot\bar{C} + A(C + B) $$ 
Thanks
 [/INST] Picking up where you (initially) left off (your work thus far is correct, save for the last line were you remove $\overline B$)...
$$\begin{align} &\overline{A}\cdot\overline{B}\cdot\overline{C} + A\cdot\overline{B}\cdot C + A\cdot B\cdot \overline{C} + A \cdot B\cdot C \\ \\
&\vdots \\ \\
&=\overline A \cdot \overline B \cdot \overline C + A(\overline B\cdot C+B) \\ \\
& = \overline A \cdot \overline B \cdot \overline C + A\cdot \overline B \cdot C + AB\tag{as good as it gets!}\\ \\ 
& = \overline B(\overline A \cdot \overline C + A\cdot C) + AB\tag{doesn't help any}\\ \\
\end{align}$$
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