1. ## Boolean logic Simplification

Would someone be so kind and explain to me how to simplify this expression I have attached. I have a rough idea but wanted to confirm the right way of going about this..

$\overline{A}~\overline{B}+A\overline{B}=( \overline{A}+A)\overline{B}=\overline{B}$
$\overline{A}C+C = (\overline{A}+1)C=C$
$\overline{A}~\overline{B}+\overline{A}C + C + A\overline{B}=\overline{B}+C$