Construct a finite automaton that accepts {0, 1}*

Recall a set A is countable if |N| ≥ |A|. Recall that Cantor’s theorem shows that P(N) = {X ⊆ N}is uncountable. Prove this.Show that F = {X ⊆ N | |X| < ∞} is countable, with an onto functiong : N → F that is computable.   Write a program/function (e.g., in Python) that runs forever and prints every element of F,e.g., if run it would print something like{0}{1}{0,2}{3}{0,2}{0,5,7}{1}{0,1}{}{2}...(Note that you must prove that the program works, i.e., it prints every element of F, and onlyelements of F.)

What is the union of sets {1,3,4} and {0,3,5}?