The SCOPE of a quantifier is the extent of the function which it governs.

If a quantifier is followed by a ~ or another quantifier, then its scope is the same as that of the following ~ or quantifier.

If a quantifier is followed by a (, [, or { then its scope extends to the associated ), ], or }

If a quantifier is followed by a capital letter, then its scope extends to the end of the simple proposition, to the next nonletter.

A quantifier BINDS a variable in its scope if the variable letter is in the quantifier.

In (x)(Fx ⊃ Gy), x and y are in the scope of the quantifier but only x is BOUND by it. And, in (x)Fx ⊃ Gx, the x in Gx is not bound.

In a correct translation, every variable is in the scope of a quantifier which binds it. A variable not bound by a quantifier is said to be FREE. That is, in a correct translation no variable is free.

Example: