Question 2
$S \left[A\right]$ is the sum of all elements over all subsets of $A$, including the empty set. For $A = \{ 1 , 2 \} , S \left[A\right] = 6$. $a$)Find $S \left[\{ 1 , 2 , 3 \}\right]$. $b$)For four distinct natural numbers $C = \{ a , b , c , d \}$, prove $8$ divides $S \left[C\right]$.