The even$-$concatenation operation, denoted as A$**,$ is applied to a set A$,$ representing the set of all

possible even$-$length combinations formed by concatenating zero or more elements from A$.$ It includes

the empty string and all even$-$length combinations of elements from A$.$ If A $=\{0,1\},$ then A$**$ includes

strings like $,00,01,10,11,0000,0011,1100,$ etc. Notice that A$**$ is an infinite set.

Question $2\mathrm{.}2$

C is a countably infinite set. Prove or disprove that C

$**$ is countable. $($Hint: You may use unique

prime factorization$)$