If you are in a course that requires you to understand the proof of part A, then it is absolutely improvement for YOU to find a proof for yourself. There are many ways to do this problem. Most of them require the following theorem: “A countable union of countable sets is countable”. One way I like to approach this problem is to prove this: “For each n, prove the set of all n-tuples of integers is countable”. For example any triple (3-tuple) of integers corresponds to a polynomial of degree of at most two with integer coefficients. Thus the set A is countable; there is a one-to-one correspondence between elements of set A and elements in set B; B is also one-to-one to C.