Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Proving transitivity, stuck at at algebra

  1. Dec 12, 2009 #1
    1. aRb on Z if 5|2a+3b



    2. Since 5|2a+3b, 2a+3b=5m, so 2a=5m-3b.



    3. Consider 3a+2b=2a+2b+a=5m-3b+2b+a=5m-b+a. I can't show that 5 divides that, but there is another way to wrangle that into a better form. I need help seeing how that works. Thanks.
     
    Last edited: Dec 12, 2009
  2. jcsd
  3. Dec 12, 2009 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    For transitivity you are given aRb and bRc and need to show aRc. You haven't even introduced c yet, nor written in terms of a and c what you have to show.
     
  4. Dec 12, 2009 #3
    Re: proving SYMMETRY, stuck at at algebra

    Sorry. I'm trying to show symmetry, not transitivity.
     
  5. Dec 12, 2009 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hint: What happens if you subtract 5a and 5b from your equation 2a + 3b = 5m?
     
  6. Dec 12, 2009 #5
    Good things happen. I think I can write: Assume aRb. Then 5|2a+3b iff 5|-(2a+3b) iff 5|-2a-3b iff 5|-3b-2a+5b+5a iff 5|2b+3a. Now aRb implies bRa, thus R is symmetrical.

    I'll sleep on that. Many thanks!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook