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Homework Help: Disprove the nested quantifier

  1. Feb 20, 2013 #1
    1. The problem statement, all variables and given/known data
    ∃x∀y(y̸=0→xy=1) in the real numbers universe.

    2. Relevant equations

    3. The attempt at a solution
    Since the given statement is false I negated the whole statement to become

    ∀x∃y(y̸!=0^xy!=1) (!= means not equal to)

    then I would have to prove this correct by setting y to something except zero
    I cant find any y to prove this correct
  2. jcsd
  3. Feb 20, 2013 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    I can't make sense of your formulae. I think you messed up the typesetting. Also, it may help to use words instead of symbols... especially if you have to improvise to make the symbols.
  4. Feb 20, 2013 #3
    there exists an x,for every y (if y does not equal to zero then x*y=1)

    *real numbers universe
  5. Feb 20, 2013 #4


    Staff: Mentor

    How about this?

    For every nonzero y in R, there exists an x in R such that xy = 1.
  6. Feb 20, 2013 #5
    i have to disprove the statement since it is false
  7. Feb 20, 2013 #6


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    Science Advisor
    Homework Helper

    If y does not equal 0, then there is only one value x such that x*y=1. That's x=1/y. How can there be an x that has an infinite number of solutions to x*y=1?
  8. Feb 20, 2013 #7
    Exactly why the statement is false, but i have to prove that it is false
    by negating the whole expression
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