Simplifying a boolean expression to not need a or gate
You just need to know that \$A+B=\overline{\overline{A+B}}=\overline{\overline{A}\cdot\overline{B}}\$. So:

$$\begin{align*} A\cdot B\cdot C + A\cdot\overline{B}\cdot\overline{C} + A\cdot B\cdot\overline{C} &amp;\\\\
&amp;=\overline{\overline{A\cdot B\cdot C + A\cdot\overline{B}\cdot\overline{C} + A\cdot B\cdot\overline{C}}}\\\\
&amp;=\overline{\overline{A\cdot B\cdot C}\cdot\overline{A\cdot\overline{B}\cdot\overline{C}}\cdot\overline{A\cdot B\cdot\overline{C}}}
\end{align*}$$

Of course, you could have first simplified your equation. It's just \$A\cdot B + A\cdot\overline{C}\$.