Chapter 11.2, Problem 3ES

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

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