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Technically, there are several sets of possible "primary
colors." A set of primary colors can be loosely defined as
three colors, that when mixed, produce all the other colors in
the rainbow.
Cyan, Magenta, Yellow is a primary set,
and so
is RGB, which is the complment of CMY.
Presumably one could
define orange, green, violet (the compliments of RYB) as a
"primary" set.
There is no compelling physical reason to
favor any of these options over another.
I have no problems with teachers calling RYB "primary colors",
since this is the common designation of primary colors in art
classes.
. Some color-mixers give the
options of working with an RGB system, a CMYK system, a color
wheel system, or a hue-saturation-brightness (HSB) system.