# Proving statements true or false.

• Sep 17th 2009, 02:40 PM
GreenDay14
Proving statements true or false.
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.
• Sep 17th 2009, 03:13 PM
Plato
Quote:

Originally Posted by GreenDay14
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.

A is false. Think $\frac{1}{2}$ and the fact that any integer is even or odd.

B is true. $q = \frac{m}{n}\, \Rightarrow \,m = nq$
• Sep 17th 2009, 03:18 PM
GreenDay14
thank you very much for the prompt reply, however I am having a bit of trouble understand what you mean in A. Would it be possible to elaborate a bit?
• Sep 17th 2009, 03:27 PM
Plato
Quote:

Originally Posted by GreenDay14
thank you very much for the prompt reply, however I am having a bit of trouble understand what you mean in A. Would it be possible to elaborate a bit?

Why don't you work on the problem for yourself?
What do you know about rational numbers?

I will not hand you a ready to turn in solution.
• Sep 17th 2009, 03:29 PM
GreenDay14
I am not asking for a ready to turn in solution, I want to better understand what you are presenting me so I can work it out for myself. It is also noteworthy that I am doing this as spare work, I am not being graded on it.
• Sep 17th 2009, 03:31 PM
Plato
Quote:

Originally Posted by GreenDay14
I am not asking for a ready to turn in solution, I want to better understand what you are presenting me so I can work it out for myself. It is also noteworthy that I am doing this as spare work, I am not being graded on it.

Well, good luck.
• Sep 17th 2009, 03:32 PM
GreenDay14
lol wow, I appreciate the kind and courteous hospitality...