″Relevant public″ is a kind of legal fiction in trademark law. In China, Germany, France, the European Union, and the World Intellectual Property Organization (WIPO), ″relevant public″ is regarded as an important legal concept when construing the distinctive characters of trademark, the identification of well-known trademarks and the assessment of trademark confusion. Consequently, it is important to analyze the definition and the composition of this concept. This paper discusses how to dissect the definition and the composition of ″relevant public″ by legal reasoning. The analysis of these issues is carried out in four steps. Firstly, to clarify the major premise, this paper dissects the concept of ″relevant public″ in the trademark legislation of diverse countries. Secondly, to focus on the key point of legal reasoning, this paper analyzes the composition of ″relevant public″. Thirdly, this paper summarizes and analyzes the major factors of analyzing ″relevant public″ in typical trademark cases of China. Finally, to define the contours of ″relevant public″ in specific cases, this paper builds an analysis model of ″relevant public″ using the mathematical set theory. To summarize the concept of ″relevant public″, as it applies to the relevant legislation discussed in this paper, this paper holds that ″relevant public″ refers to consumers who are associated with the commodity and service marked by trademark, and business operators who are associated with the commodity and service intimately marked by trademark. As for the composition of ″relevant public″, this paper holds that it is mainly related to the consumers and business operators. Consumers include both real consumers and potential consumers, they also include both natural and legal persons. Business operators refer to the merchants selling the commodity and service identified by trademark, and business operators in the marketing process of said commodity and service. With respect to the delimitation factors of the ″relevant public″, this paper identifies the ″nature and characteristics of commodity and service″ and the ″regional scope covered by commodity and service″ as two core factors. The ″regional scope covered by goods and services″ refers to the regional scope actively covered or passively spread by the commodity and service in a specific time. It includes not only the physical area where the commodity and service are actually located, but also the information transmission area. The ″nature and characteristics of commodity and service″ includes but is not limited to category, purpose, price, and other factors. Finally, this paper constructs an analysis model of ″relevant public″ by using the mathematical set theory. This model applies the quantitative analysis method to identify the subset of each factor and then discusses the relationship of two subsets. In the end, this model shows the final contours of ″relevant public″ in a model case. The innovation of this paper lies in two aspects. The first aspect is the research method. This paper uses the mathematical modeling method and mathematical set theory to analyze a legal concept. This paper builds an analysis model of ″relevant public″ by applying the mathematical set theory. Using this model, this paper applies the quantitative assessment method to two core factors: the ″nature and characteristics of commodity and service″ factor and the ″regional scope covered by commodity and service″ factor. Following that application, this paper then discusses the relationship between the subsets of the two factors and the scope of their intersection. Lastly, this paper concludes with the ideal method and path to identify the ″relevant public″ scope in a specific time. The second aspect is the research conclusion. This paper discusses the essential connotation of ″relevant public″, and analyzes the composition subjects of this concept. It identifies ″relevant public″ as a legal fiction which refers to consumers who are associated with the commodity and service marked by trademark, and business operators who are associated with the commodity and service intimately marked by trademark. By summarizing typical trademark cases in China, the paper analyzes the core factors of identifying the scope of the ″relevant public″. Finally, after constructing the ″relevant public″ analysis model, the paper concludes by determining the scope of ″relevant public″in a model case, which has strong practicability.