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Math Help - Proving statements true or false.

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by GreenDay14 View Post
    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
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    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?
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    Quote Originally Posted by GreenDay14 View Post
    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.
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    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.
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    Quote Originally Posted by GreenDay14 View Post
    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.
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    lol wow, I appreciate the kind and courteous hospitality...
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