Each number of the set $\{1,2, 3,4,5,6, 7,8\}$ is colored red or blue, following the following rules: (a) Number $4$ is colored red, and there is at least one blue number, (b) if two numbers $x,y$ have different colors and $x + y \le 8$, so the number $x + y$ is colored blue, (c) if two numbers $x,y$ have different colors and $x \cdot y \le 8$, then the number $x \cdot y$ is colored red. Find all the possible ways to color this set.