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English into logic statement

  1. Jan 23, 2016 #1
    1. The problem statement, all variables and given/known data
    Express the following English sentence as a symbolic statement.
    Do not use the there exist symbol
    “There is a unique natural number n which is both even and prime.”

    We also have properties like
    let P(n) be the property that n is prime, L(n, m) the relation that n < m, and E(n) the property that n is even.
    3. The attempt at a solution
    [itex] \forall n (E(n) and P(n) and n<3) [/itex]
     
  2. jcsd
  3. Jan 23, 2016 #2
    Perhaps I'm under-thinking this: 2.

    It doesn't convey all the information of the original, but any sentence that does will evaluate to 2. And most will reduce to 2 as well.
     
  4. Jan 23, 2016 #3

    PeroK

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    What about first changing the English version into saying what is not true?

    I interpret your symbolic statement (attempted solution) to mean: all natural numbers are even, prime and less than 3.
     
  5. Jan 23, 2016 #4

    haruspex

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    How do you write that in symbols?
     
  6. Jan 23, 2016 #5
    Would it work to say that [itex] n \in \mathbb{N} [/itex]
    [itex] n \in \mathbb{N} : (P(n) \& E(n)) [/itex]
     
  7. Jan 23, 2016 #6

    haruspex

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    No, you must represent "there is" somehow. Are you not aware of a symbol for that?
     
  8. Jan 23, 2016 #7
    the only symbol I am aware of is there exists [itex] \exists [/itex] but we were told tonot use it in the problem.
    Im not sure of a symbol for that
     
  9. Jan 23, 2016 #8

    haruspex

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    Sorry, I overlooked that.
    In that case, as others have suggested, you can get around it by making explicit reference to that number. One part of your answer will express that 2 has these properties. What will the rest of your answer state?
     
  10. Jan 24, 2016 #9

    PeroK

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    It seems an obvious approach to me that if you're given a statement "there exists ..." and you're told not to use the ##\exists## symbol, then the first step is to rephrase the statement to avoid the phrase "there exists". That, it seems to me, is logical!

    As a start, you could think of a statement like "not all primes are odd". This starts to take you in the right direction, I believe.
     
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