I want to know the definition of null quantification and when and why we need to use it. In a book I was learning, it says:
"establish rules for null quantification that we can use when a quantified variable does not appear in part of a statement. "
" Establish these logical equivalences, where x does not occur as a free variable in A. Assume that the domain is nonempty.
a) $\forall x ~( P(x) \lor A ) \iff ( \forall x~P(x) ) \lor A$ "
Now can anyone explain me what is said in this two quotes. And what's the $A$ here in the second quote. Is this stands for a proposition without $x$ or a free variable or a bound variable.
Please explain this with a proper definition and a clear example.