Ah yes ... if that's what you'd like .. the general rule of thumb is left to right following your first post and mine below it ... it'd be read as follows ...

For all airlines there exists some flight such that flight f is in airline a

for all m there exists some k such that k is greater than m

and

there exists some flight for all airlines such that flight f is in airline a

there exists some k for all m such that k is greater than m

it's about how things are restricted and when .. imagine a bottle neck ... the second statement bottlenecks you really fast and opens up ... while the first statement narrows as you progress through. When I first learned quantifiers I learned them in the context of true and false ...

Definition. Universal quantifier, $\displaystyle \forall x \in X) P(x)$ Let $\displaystyle P(x)$ be a formula in one variable with universe U. Let $\displaystyle X \subseteq U$. Let Q be the statement

( $\displaystyle \forall x \in X$ ) $\displaystyle P(x)$

Then Q is true if for every $\displaystyle a \in X$, $\displaystyle P(a)$ is true. Otherwise Q is false.

Definition. Existential quantifier, ($\displaystyle \exists x \in X$) $\displaystyle P(x)$ Let $\displaystyle P(x)$ be a formula in one variable with universe U. Let $\displaystyle X \subseteq U$, $\displaystyle X \neq \emptyset$ . Let Q be the statement

( $\displaystyle \exists x \in X$)$\displaystyle P(x)$

Then Q is true if there is some $\displaystyle a \in X$ for which P(a) is true. Otherwise Q is false. [/tex]

This might help you a bit to see them ... I can add some more stuff if you'd like