In this paper the topic known to biologists as population genetics is presented in terms of the Cartesian product. The gene, being a set of an ordered pair of elements (alleles), provides an example of a lattice in which the axes represent the composition of the gene in respective parents, and shows as co‐ordinates the possible genetic composition of individuals of the next generation with respect to that gene. When the axes are made to represent, respectively, the set of male and female parents of a population as a whole then it is the next generation as a whole that is represented by the co‐ordinates.