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.