Animation illustrates color addition and subtraction.
In the addition choice you could imagine the primary colors red, green and blue to be projected on to a white screen. The rest of the screen is unilluminated and hence black; The region where they overlap gets a different color which depends on which two colors overlap and their brightness levels. If the brightness levels are equal you could write

Red + Green + Blue = White
Red + Green = Yellow
Green + Blue = cyan
Red + Blue = Magenta

In subtraction, you could imagine the colors Cyan, Yellow and Magenta to be painted on a white paper. White light goes through these transparent colors each of which acts as a filter removing a certain color as light passes through it and after striking the paper passes through it again. If all the three colors red, green and blue are filtered out of the white light the overlap area is black.
If the transparency levels of all paints are equal you could write

Cyan +Yellow + Magenta = Black
Yellow + Magenta = Red
Magenta + Cyan = Blue
Cyan +Yellow = Green

In fact you could see cyan as minus red, yellow as minus blue and magenta as minus green meaning cyan painted on a white paper filters out the red component of white light incident on it, yellow removes blue and magenta removes green. So the first of these equations should mean that red, blue and green are removed from the incident white light striking the white surface on which these overlapping colors are painted, and that of course should be black.

Cyan = White - Red
Yellow = White - Blue
Magenta = White - Green

Overlap of all three paints, filters out red, green and blue colors from incident light and thus makes the area of overlap black.