Abstract
Since 2009, In France, Logic as been explicitly introduced in High School as a subject to taught; however, the recommendation are to teach it not as a separate chapter, but all along the year in the different chapters of the program. The way to implement this part of the program raises several questions. In this paper we propose activities that have been experimented in the classes (grade 10) of the first two authors; these activities have been analysed for their professional dissertation in the frame of the teacher training program for prospective secondary teachers in mathematics in the ESPE Languedoc-Roussillon. The focus was on the relationships between natural logic and mathematical logic in the case of implication, considering the deduction rules and taking in account quantification matters Keywords. Natural versus mathematical logic, implication, converse, inference rules, implicit quantification, mathematics in grade 10