#1
A book I'm reading on theory claims a rule:

Chord I can be replaced by III minor 7 or IV minor 7 (which is of course the relative minor 7).

This doesnt make sense, IV isnt the relative minor, VI is correct?

Then it gives example:

In key of C C major can be replaced with Em7 or Am7.


Now Am7 is the vi (relative minor). This is a misprint correct?

Both the I chord, and the vi chord can be replaced with the VI minor 7th?
#2
the example it gives is correct, all the notes of the Em7 and Am7 are in the key of C major

edit: A IS the relative minor of C major, as for "replacing" the I with the III or IV i'm not sure what context they are referring to but it appears that everything written about what can be done is accurate.
#3
In the major scale:

I III and VI have the same chord function.

As do II and IV, and V and VII.

This is a bit of Jazz theory, that really there are only three chords in the major scale using like function substitution.

I think that book had a misprint, IV should have been VI.
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#4
Yeah, the book mentions exactly what you said, except you have to modify the chords with 7th's or used dim/aug type stuff that I'm just diving into.

Thanks for the help sir!