According to the intuitive definition of combination of logics, the combination of two logics is the smallest conservative extension of both on the combined language. Combining the logic of conjunction with the logic of disjunction by using obvious methods (combination of their Gentzenian rules of their truth-tables) leads to a logic in which distributivity holds, such a logic therefore cannot be considered as the proper combination of the logics of conjunction and disjunction. In this talk I will present several methods to combine properly these two logics: combination of neo-Gentzenian systems, product of matrices and use of non-distributive matrices. Joint work with Ana Teresa Martins.