Theory. Modes, Part Two point five (2.5)

A couple of posts back I asked myself (and any readers) the following question: w
hat are the I, II and V 7th chords of F major?


Here's the answer:
I.     F major 7th
II.    G-7, aka, G minor 7th
V.    C7, aka, C dominant


The logic goes like this. For 7th chords,
- the I chord is always major, thus consisting of a major 3rd and a major 7th,
- the II chord is always minor, thus consisting of a minor 3rd and a minor 7th,
- the V chord is always a dominant, thus consisting of major 3rd and a minor 7th.
The actual note values are:


F major 7th
  - F, A, C, E

G minor 7th

  - G, B-flat, D, F

C dominant 7th
  - C, E, B-flat, G

OK, so what does this have to do with modes?  Still working on that.