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Quick question on sets

  1. Aug 18, 2005 #1
    Hi I'm just wondering how I would sketch the following, it's part of a subspace question.

    H = {(x,y) : xy = 0}

    I don't thinking dividing my x will do that much. If x is not equal to zero then dividing by x gives me y = 0. But what would happen for points (x,y) where x = 0?

    It's one of the questions in my question booklet, not an assignment question. I wouldn't post an assignment question on the internet. Any help would be appreciated.
    Last edited: Aug 18, 2005
  2. jcsd
  3. Aug 18, 2005 #2


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    Well, [itex]xy = 0 \Leftrightarrow x = 0\,\, \vee \,\,y = 0[/itex]
  4. Aug 18, 2005 #3
    I am not familiar with the notation that you have used. Does the v mean "or?" Thanks for the help.
  5. Aug 18, 2005 #4


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    Homework Helper

    Yes, indeed.
    A product of two factors is 0 iff at least one of them is 0.

    If x isn't zero, you can divide by x and find that y has to be zero.
    If y isn't zero, you can divide by y and find that x has to be zero.
    In the last case both are zero, and then you have the element (0,0)
  6. Aug 18, 2005 #5
    Thanks again, what you've said makes sense.
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