In this talk we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logic of disjunction (LD) and the logic of conjunction (LC). At first it seems that it would be very easy to combine such logics, but the following problem arises: if we combine LC and LD in a straightforward way, distributivity between both connectives holds. On the other hand, distributivity does not arise if we use the usual notion of extension between consequence relations. The spontaneous generation of distributivity is in fact a paradox and a problem, because the standard view of combination of logics is that the combined logic is the smallest one defined on the combined language, which extends the two combined logics. One could think that there is no paradox because the logic of conjunction and disjunction is necessary distributive, but also someone who knows a bit of lattice theory is aware that non-distributivity is perfectly possible. An analogous phenomenon occurs with the so-called absorption laws, which are generated by the straightforward combination of logics LC and LD and they are valid even in the logic of lattices. On the other hand, these laws do not hold in the least extension of LC and LD. A detailed discussion about this phenomenon, as well as some elucidation for it, is given. This is a join work with Jean-Yves Béziau.