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Math Help - universe of discourse

  1. #1
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    universe of discourse

    determine whether it is true when the universe of discourse to be R and using only symbols from the following list,,
    this question is about AND OR conjunction ,disjunctions,,
    details about question are in the attachment,,
    i can't type the symbols,,
    so plz read the attachments,,
    any help is appreciated.
    thank you
    Attached Thumbnails Attached Thumbnails universe of discourse-question.bmp  
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  2. #2
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    Quote Originally Posted by ives View Post
    determine whether it is true when the universe of discourse to be R and using only symbols from the following list,,
    this question is about AND OR conjunction ,disjunctions,,
    details about question are in the attachment,,
    i can't type the symbols,,
    so plz read the attachments,,
    any help is appreciated.
    thank you
    For all who cannot read the attachement it says
    \left( {\forall x} \right)\left( {\exists y} \right)\left[ {\left( {x = yy} \right) \vee \left( {yy + x = 0} \right)} \right]
    Is that true on the domain, \mathbb{Z} or on \mathbb{R}.
    On \mathbb{Z} let x=-3. Is it true?

    What about on \mathbb{R}?
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  3. #3
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    i get a question, is the domain for x=yy affect the domain of yy+x=0
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  4. #4
    Senior Member MacstersUndead's Avatar
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    x = yy has all real numbers as its domain.
    yy + x = 0 <=> x = -yy has all real numbers as its domain as well.

    (graph these parabolas for a graphical arguement)
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  5. #5
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    domain for x=yy can't be all real numbers , cuz yy>=0
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  6. #6
    Senior Member MacstersUndead's Avatar
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    Sorry, let me add an extra step.

    If the domain refers to the x-axis, then all the real numbers are the domain (no restriction on x)
    The range would then be the y-axis, which has a limitation, which you mentioned to be yy>=0, or specifically, that y > 0.
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