I converted from a truth table to sum of products and simplified that easily. What I am having problems with is simplifying the product of sums for that same truth table. I have:
NOTE: $A' = \text{not} A$
$$(A+B+C)(A+B+C')(A+B'+C)(A'+B+C)$$
which I have simplified to (so far):
$$A + AB + AC' + B + BC' + AC + BC + A'B' + B'C + A'C + C$$
which I know should simplify to:
$$AB + BC + AC$$
I have used the Boolean algebra rules that I know, I just need help learning the rules that I don't know.
Thanks!
Best Answer
$$\begin{align} (A+B+C)(A+B+\overline C)(A+\overline B + C)(\overline A+B+C) &=\\ (A+B+C\overline C)(A+\overline B + C)(\overline A+B+C) &=\\ (A+B)(C+(A+ \overline B)(\overline A + B)) &=\\ (A+B)(C+AB+\overline A \cdot \overline B) &=\\ AC + AB + 0 + BC+AB + 0 &=\\ AB + BC + AC&\end{align}$$