Textbook Problem

The following is a formal definition for O-notation, written using quantifiers and variables: $f\left(n\right)$is $O\left(g\left(n\right)\right)$if, and only if, $\exists$ positive real numbers b and B such that $\forall n\ge b,0\le f\left(n\right)\le Bg\left(n\right)$ .

a. Write the formal negation for the definition using the symbols $\forall$ and $\exists$ .
b. Restate the negation less formally without using the symbols $\forall$ and $\exists$ or the words “for any,” “for every.” or “there exists.”