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Need help with this Proof

  1. Sep 27, 2009 #1
    Show that these statement about real number x are equivalent
    (i) x is rational
    (ii) x/2 is rational
    (iii)3x-1is rational

    i think you have to use contradiction but i don't know how
  2. jcsd
  3. Sep 27, 2009 #2


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    x is rational if and only if you can write it in the form p/q for p, q integers (and q non-zero). So if x is rational, let x=p/q. Can you find integers m and n such that x/2=m/n? You can do this exact process to show that 1 implies 2, 2 implies 3, and 3 implies 1 (which gives that they are equivalent)
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