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Predicate logic implication and quantifiers

  1. Nov 19, 2007 #1
    1. The problem statement, all variables and given/known data

    C = (Ax)(EY) (p(X) -> p(Y))

    D = (EX)(Ay) (p(X) -> p(Y))

    Are C and D equivalent?

    2. Relevant equations

    Truth table for implication

    T T -> T
    T F -> F
    F T -> T
    F F -> T

    3. The attempt at a solution

    Well I believe C is true is all cases and is a tautology whilst D is not true.

    C is true as you can set y = x to make p(Y) true if P(X) is true if x and y belong to the same set.

    D is false for example if have p{n | n is prime}, and have x is 3 then p(X) will be true but for all y if x and y belong to N then some p(Y) will be false making the formula overall false.

    Is this correct? Has anyone got any tips on whether this is right?
  2. jcsd
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