Definition:Subordinate

Definition
Let $\mathbf C$ be a WFF of propositional calculus.

Let $\circ$ and $\ast$ be connectives.

Then $\circ$ is subordinate to $\ast$ iff the scope of $\circ$ is a well-formed part of the scope of $\ast$.

Example
Consider the propositional WFF:


 * $\mathbf A := ((P_0 \land P_1) \implies ((P_2 \lor \neg P_3) \land (P_4 \iff P_5)))$

It is left as an exercise to the reader to demonstrate that $\mathbf A$ is well-formed.

The following statements are also left as exercises to prove:


 * The main connective of $\mathbf A$ is $\implies$. Therefore the scope of $\implies$ is $\mathbf A$.


 * The substring:
 * $\mathbf B := ((P_2 \lor \neg P_3) \land (P_4 \iff P_5))$
 * is a well-formed part of $\mathbf A$.


 * The main connective of $\mathbf B$ is $\land$. Therefore the scope of $\land$ (the second occurrence of it in $\mathbf A$, of course) is $\mathbf B$.


 * The connective $\iff$ is subordinate to the occurrence of $\land$ in $\mathbf B$, but not to $\lor$ or $\neg$.

And so on.