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?
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.
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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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!