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Examples

• (forall x: y <= x)
  • x is bound, y is free; the formula is therefore not closed.
  • true in assignment [y |-> 0] over the domain of natural numbers with the usual interpretation of ` <= `, because 0 <= x is true for every natural number x:

    0 <= 0, 0 <= 1, 0 <= 2, ...

• (exists x: x | 15)
  • x is bound; the formula is closed.
  • true for every assignment over the natural numbers with `|' interpreted as `divides', because x | 15 is true for some natural number x (e.g. for 3):

    3 | 15.