Question

Tough Algebra proof, no idea where to begin. Picture posted below

Answer 1

Help

Answer 2

Anyone, any insight would be great

Answer 3

We have to prove that for every set A there can be only 2^A subsets
correct?

Answer 4

We have to prove that the cardinality (size) of A is less than the set of all it's subsets (2^A). The first part is easy but I have no idea what to do with the U = U_b and U_a

Answer 5

Can you show me how to did the first part

Answer 6

I defined an arbitrary function g: A -> 2^A s.t. g(x) = {x}
if x is an element of A then {x} will be an element of 2^A since by definition it is the set of all subsets of A and {x} is a subset

Answer 7

g is injective since there always exists a unique set {x} for every element