I was confused a little about the def q0, q1, q2, q3 sets.

Here is my attempt to define "not all", "any", "all" and "not any":

1. q0: Not all: Not all the elements belong in the set.
But does that not translate into at least one element belongs in the set?

2. q1: Any: If there exists at least one element in the set.

3. q2: All: If every element belongs in the set.

4. q3: Not any: All the elements do not belong in the set.

Any insight?

Update:
Probably should not reword "not all".
On one of the lecture slides, the difference between q0 and q1 were matched with the statements "Some female employee earns over 42 000" and "Some male employee does not earn over 42 000" respectively.
For future reference: Notice which statement means 'not'.