Contrapositive, Converse and Inverse of statements with multiple quantifiers My textbook only touched on negation of statements with multiple quantifiers, and I would like to know:

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*For a statement like
$\forall M>0, \exists \delta > 0$ such that if $0 < |x-a| < \delta$ then $|f(x)| > M,$
is its contrapositive
$\forall M>0, \exists \delta > 0$ such that if ~$(|f(x)| > M)$ then  ~$(0 < |x-a| < \delta)\quad?$


*Do the converse and inverse similarly just affect the if-else?

Yes, Contrapositive, Converse and Inverse all refer and apply to conditional formulae and affect only their antecedents and consequents and not any surrounding quantifier or connective.
This is not to say that they never alter quantifiers: the contrapositive of $$\forall x\big(Px\to\exists y Qxy\big)$$ is $$∀x(∀y¬Qxy→¬Px).$$ (Strictly speaking, we are referring to the contrapositive of the string within the parentheses.)
How can I know when to negate quantifiers when taking the contrapositive of a statement?
