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Translating into first order predicate expressions

  1. Nov 8, 2007 #1
    1. The problem statement, all variables and given/known data

    I have been given the following predicates of the domain of real numbers

    2. Relevant equations

    P(x): x>0 E(x): x is even D(x): x is exactly divisable by 5

    (i) At least one integer is even
    (ii) There exists a positive integer that is even
    (iii) If x is even then x is not exactly divisible by 5
    (iv) There exists an even integer exactly divisable by 5

    3. The attempt at a solution

    (i) Ax(E(x))
    (ii) Ex(P(x) ^ E(x))
    (iii) Ax(P(x) ¬ D(x))
    (iv) Ax(P(x) U D(x))

    Any help would be greatly appreciated, as im not sure if the above is correct.

    Many Thanks
    Steve
     
  2. jcsd
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