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Which relations are symmetric

  1. Aug 16, 2012 #1
    Determine which of these relations are symmetric

    1) x~y if and only if x-y is positive
    2) x~y if and only if xy >= 0
    3) x~y if and only if x+2y is positive
    4) x~y if and only if x+y is positive
    5) x~y if and only if x+y is odd

    I thought all but 1) but this was wrong.
    The only one im sure that is symmetric is 2)
     
  2. jcsd
  3. Aug 16, 2012 #2

    HallsofIvy

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    It is certainly true that if x+ y is positive, so is y+ x.

    It is certainly true that if x+ y is odd, so is y+ x.

    What about "x+ 2y is positive"? Can you find x such that x+ 2y is positive but y+ 2x is not?
     
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