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:


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

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


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


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

And so on.