Please help me with these questions. I If it is possible to label each element of an infinite set S with a finite string of keyboard characters, from a finite list characters, where no two elements of S havethe same label, then S is a countably infinite set.Use the above statement and prove that the set of rational numbers is countable.Multiple ChoiceOWe can label the rational numbers with strings from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, /, -] by writing down the string that represents that rationalnumber in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable.We can label the rational numbers with strings from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, /] by writing down the string that represents that rationalnumber in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable.OWe can label the rational numbers with strings from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -] by writing down the string that represents that rationalnumber in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable.OWe can label the rational numbers with strings from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, /, -] by writing down the string that represents that rationalnumber in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable. The set A x Z* where, A = (2, 3) (Check all that apply.)Check All That ApplyThe set is countable.The set is countably infinite with one-to-one correspondence 1 → (2,1), 2 ↔ (3,1), 3 ↔ (2,2), 4 ↔ (3,2),and so on.The set is countably infinite with one-to-one correspondence 0 ↔ (2,1),1 ↔ (3,1), 2 ↔ (2,2), 3 → (3,2), and so on.The set is uncountable.

As per the guideline, I am supposed to solve only first question from the given problems.Given that…

If it is possible to label each element of an infinite set S with a finite string of keyboard characters, from a finite list characters, where no two elements of Shave the same label, then S is a countably infinite set. Use the above statement and prove that the set of rational numbers is countable.