In the scenario you've described, Box A appears black and Box B appears red when illuminated by red light. This can be explained by the properties of light absorption and reflection.
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Box A (Black): A black object absorbs all colors of light (including red) and reflects none, which is why it appears black under red light.
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Box B (Red): A red object reflects red light and absorbs all other colors. Thus, it appears red when illuminated by red light.
Based on this understanding, the correct statement would be:
Box A absorbs red light, and Box B reflects red light.
So the correct answer is: Box A absorbs red light, and Box B reflects red light.