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Math Help - Syntax of First-Order Predicate Logic

  1. #1
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    Syntax of First-Order Predicate Logic

    It seems like a trivial question, but does changing the order of the variables within parentheses in a quantified wff change the meaning or truth value? For example:

    x y P( x, y) VS. ∀ x y P( y, x)

    From what I gathered on my own, I didn't think this slight change made a difference to the wff, but I want to be sure to avoid making any sort of mistake. Thanks!
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  2. #2
    Senior Member
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    Dec 2008
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    yes this change could make a difference if for example P(x,y) meant that x loves y the P(y,x) would mean that y loves x which are different statments,

    if however P was the identity relation then clearly x=y is the same as y=x however this being a special case in genral this does make a difference,
    hope that helps
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