Question 10
The set $A=\{1,2\}$ has four subsets: $\varnothing,\{1\},\{2\},\{1,2\}$. Their element sums are $0,1,2,3$, respectively. Let $S[A]$ denote the sum of these sums over all subsets of $A$. Thus $S[A]=0+1+2+3=6$.
a) For $B=\{1,2,3\}$, find $S[B]$.
b) For $C=\{a,b,c,d\}$, where $a,b,c,d$ are distinct natural numbers, prove that $S[C]$ is divisible by 8.
a) For $B=\{1,2,3\}$, find $S[B]$.
b) For $C=\{a,b,c,d\}$, where $a,b,c,d$ are distinct natural numbers, prove that $S[C]$ is divisible by 8.