How was the result of this SOP (sum of products) expression reached?
Well you are making a mistake \$(\overline{A\overline{B}}) (C+\overline{C})\$ is not eaqual to what you just wrote. You can't just ignore the complement that is sitting right there. It would be equal to \$\overline{A\overline{B}}C + \overline{A\overline{B}}(\overline{C})\$

Anyway the easier thing to do this, if you already have truth table, look for the values of F when it's 1. As you can see there are 7 terms in your SOP expression and there are 7 true (or one) values in your F column.

Let's start with the first row as you can see it's \$ A= 0, B=0, C=0\$ and the value is true. We could write that as \$\overline{A}*\overline{B}*\overline{C} \$. 

Why I wrote it this way? Well since it is AND operation the only way that expression can be true is when A B C are zero. Same goes for every row except 6th one.

Let's do one more example, 7th row, \$ A= 1, B=1, C=0\$, we could write that as \${A}{B}\overline{C} \$.

Do that for every row and you have complete SOP expression.