I am having an absurd amount of trouble with what seems to be very easy questions. The question asks:

Answer true or false and supply a direct proof or a counterexample to each of the following assertions.

(a) There exists a integer n (does not equal) 0 such that nq is an integer for every rational number q.

(b) For every rational number q, there exists an integer n (does not equal) 0 such that nq is an integer.

Any help with either of these would be greatly appreciated. Thanks.