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Symbolizing with Quantifiers

  1. Oct 28, 2012 #1
    For a homework assignment I got the following as a question:

    Symbolize the following using quantifiers, predicates and logical connectives.

    For all integers n, 2n+1 is an odd integer.

    Here is what I came up with:

    O(x): x is odd
    ∀x((2x + 1) → O(x))

    Would this be the correct form?

    Thanks
     
  2. jcsd
  3. Oct 28, 2012 #2
    What I posted doesn't seem right. Maybe it should be something like this:

    O(x): x is odd
    ∀xO(2x + 1)

    Would this be correct?
     
  4. Oct 28, 2012 #3
    Also, the domain of x would be all integers.
     
  5. Oct 28, 2012 #4

    Bacle2

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    Science Advisor

    Your transcription says that for all x, if 2x+1, then x is odd. I would use:

    Domain is integers, as you said.
    O(x): x is odd
    ∀x∀y((y=2x + 1) → O(y))
     
  6. Oct 28, 2012 #5
    Yeah, that makes more sense. Now it's saying for every integer x, if y = 2x + 1, then y is always odd.

    Thanks a lot!
     
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