Which of these demonstrates the relationship of synonyms?

The relationship of synonyms is demonstrated by words that have similar meanings. In this instance, "fast" and "quick" both convey the idea of high speed and can be used interchangeably in many contexts. This similarity in meaning exemplifies the concept of synonyms, making this pair the correct answer.

Other options present contrasting or antonymous relationships. "Rough and smooth" illustrate opposites in texture, while "rich and poor" depict extremes in wealth status. Similarly, "hot and cold" express opposing temperatures. These relationships do not align with the concept of synonyms, thus reinforcing why the choice of "fast" and "quick" stands out as the correct demonstration of synonymy.