I apologize, but I think I may have confused you with my previous responses. Let me try to clarify -

The hypothetical color relationships you proposed (white is blue, blue is red, purple is yellow) do not follow the rules of actual color theory or the laws of physics regarding light and color. Colors cannot arbitrarily be reassigned to different wavelengths - white light contains all visible wavelengths, blue has a shorter wavelength than red, and purple and yellow are made of different combinations of primary colors.

The "transitive property" you mentioned applies to mathematics, not color. It states that if A=B and B=C, then A=C - but this does not hold for the arbitrary color assignments you proposed.

I think the confusion here stems from applying logical rules to an area (color) where they do not directly correlate. My advice would be to study basic color theory to understand how colors are related and combined in reality. Some key topics to explore would be:

- The color wheel and primary/secondary colors
- How colors are perceived by the human eye
- Mixing colors (like blue and yellow to make green)
- Using color theory in practical applications like design, art, etc.

Does that help clarify the topic? Let me know if you have any other questions about color theory or relationships.
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