For any function f: A → B , define a new function g: P(A) → P(B) as follows: for every S ⊆ A, g(S) = { f(x) |
x ∈ S Prove that f is onto if and only if g is onto.

Question

For any function f: A → B , define a new function g: P(A) → P(B) as follows: for every S ⊆ A, g(S) = { f(x) |
x ∈ S   Prove that  f is onto if and only if  g is onto.

Quizplus · Accepted Answer

The Answer of For any function f: A → B , define a new function g: P(A) → P(B) as follows: for every S ⊆ A, g(S) = { f(x) |
x ∈ S   Prove that  f is onto if and only if  g is onto.

For Any Function F: a → B , Define a New