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  • Any occurrence a variable in a formulate not in the scope of a quantifier is said to be a free occurrence

  • Otherwise it is called a bound occurrence

  • Thus, if x is a free variable in φ it is bound in ∀xφ and ∃xφ

  • A formula with no free variables is called a closed formula

  • Example: x and y are bound variables, z is a free variable

    ∀x∀y(P(f(x)) → ¬(P(x)) → Q(f(y), x, z)))

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