Blue flower color is produced in a species of morning glories when dominant alleles are present at two gene loci, A and B. (Plants with the genotype  have blue flowers.) Purple flowers result when a dominant allele is present at only one of the two gene loci, A or B. (Plants with the genotypes  and  are purple.) Flowers are red when the plant is homozygous recessive for each gene (i.e., aabb).

Two pure-breeding purple strains are crossed, and all the F₁ plants have blue flowers. What are the genotypes of the parental plants?