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Homework Help: Negation statement

  1. Mar 1, 2009 #1

    ([tex]\exists_{x} \in [/tex] R) ([tex]\forall_{y} \in [/tex] R) (3x + 2y = 7)

    Trying to find negation statement. This is what I think it is:

    ([tex]\forall_{x} \in [/tex] R)([tex]\exists_{y} \in [/tex] R) (3x + 2y ≠ 7)

    Is this close?
  2. jcsd
  3. Mar 1, 2009 #2
    I'm having trouble reading this notation, but I'm assuming the first statement says "There exists an x in R such that for all y in R, 3x + 2y = 7."

    To make this backwards, we would need to say, "For each x in R, there exists a y in R such that 3x + 2y does not equal 7," so if I have interpreted your notation correctly, I think your answer is correct.
  4. Mar 1, 2009 #3
    Thanks, phreak. Yes, that is how it should read.
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