For a finite set A of integers, let a (A) denote the sum of the elements of A Then if U is a finite universe taken from Z , Ap(U) (A) denotes the sum of all elements of all subsets of U Determine Ap(U) (A) for a) U 1, 2, 3 b) U 1, 2, 3, 4 c) U 1, 2, 3, 4, 5 d) U 1, 2, 3, , n e) U a1, a2, a3, , an ,...

a P 0123121323 and A p A 1 2 3 1 2 1 3 2 3 1 2 3 41 2 3 2 2 1 2 3 24 b ...

For a finite set A of integers, let a (A) denote the sum of the elements of

Question:

For a finite set A of integers, let a (A) denote the sum of the elements of A. Then if U is a finite universe taken from Z+, ∑A∈p(U) σ(A) denotes the sum of all elements of all subsets of U. Determine ∑A∈p(U) σ(A) for
a) U = {1, 2, 3}
b) U = {1, 2, 3, 4}
c) U = {1, 2, 3, 4, 5}
d) U = {1, 2, 3, ..., n}
e) U = {a1, a2, + a3, ..., an}, where
s = a1 + a2 + a3 + ∙ ∙ ∙ + an