Question 5
The set $A=\{1,2\}$ has four subsets: $\varnothing$, $\{1\}$, $\{2\}$, $\{1,2\}$. Their element sums are $0,1,2,3$. Write $S[A]$ for the sum of the element sums over all subsets of $A$; thus $S[A]=0+1+2+3=6$.
a) Let $B=\{1,2,3\}$. Find $S[B]$.
b) Let $C=\{a,b,c,d\}$, where $a,b,c,d$ are distinct nonnegative integers. Prove that $S[C]$ is divisible by $8$.
a) Let $B=\{1,2,3\}$. Find $S[B]$.
b) Let $C=\{a,b,c,d\}$, where $a,b,c,d$ are distinct nonnegative integers. Prove that $S[C]$ is divisible by $8$.