Definition:Abbreviation of WFFs of Propositional Logic/Rules

Rules for Abbreviation of WFFs
The following rules allow WFFs of propositional logic to be abbreviated so as to make them more readable.


 * $(1): \quad$ The outermost brackets of a WFF need not be written.


 * $(2): \quad$ Brackets can be removed around parts of nested WFFs if the inner WFF has a higher precedence than the outer one.


 * $(3): \quad$ In the case of repeated $\land$ or $\lor$ connectives, we can replace:
 * $\left({\left({\mathbf A \land \mathbf B}\right) \land \mathbf C}\right)$ with $\left({\mathbf A \land \mathbf B \land \mathbf C}\right)$


 * but not
 * $\left({\mathbf A \land \left({\mathbf B \land \mathbf C}\right)}\right)$ with $\left({\mathbf A \land \mathbf B \land \mathbf C}\right)$
 * (there is a reason for this).

Any string obtained from a WFF $\mathbf A$ by applying any of the above rules is called an abbreviation of $\mathbf A$.

The resulting strings are not actually WFFs as such, but can be translated back uniquely into full WFFs.