Definition:Scope of Connective/Definition 1

Definition
Let $\LL_0$ be the language of propositional logic.

Let $\circ$ be a connective of $\LL_0$.

Let $\mathbf W$ be a well-formed formula of $\LL_0$.

The scope of an occurrence of $\circ$ in $\mathbf W$ is defined as:
 * the smallest well-formed part of $\mathbf W$ containing this occurrence of $\circ$.

where:
 * smallest means the well-formed part of $\mathbf W$ whose length is least
 * containing means such that it is a substring of $\mathbf W$.

Also see

 * Definition:Main Connective