Final answer:
True-breeding varieties of pink snapdragons cannot be established because pink snapdragons are a result of incomplete dominance and produce offspring with a 1:2:1 phenotypic ratio of purple to pink to white flowers when crossed.
Step-by-step explanation:
The establishment of a true-breeding variety of pink snapdragons would not be possible because pink snapdragons are the result of incomplete dominance in flower color inheritance. This means that when a snapdragon with a dominant purple-flower allele is crossed with one having a recessive white-flower allele, the resultant phenotype in the F1 generation is pink, a blend of white and purple.
However, when pink snapdragons are self-pollinated or crossed with one another, the offspring will segregate again in a phenotypic ratio of 1 purple: 2 pink: 1 white, indicating that true-breeding pink snapdragons cannot be achieved as they do not breed true for the pink phenotype in subsequent generations.
In the context of Mendelian genetics and experiments with garden peas, true-breeding plants are ones that, when self-fertilized, only produce offspring with the parental phenotype. With incomplete dominance, such as that seen in pink snapdragons, self-fertilization does not produce true-breeding offspring for the heterozygous phenotype because the dominant and recessive alleles segregate in the F2 generation, resulting in the reappearance of the pure-breeding parental phenotypes as well as heterozygous phenotypes. Therefore, a true-breeding strain of heterozygotes (pink snapdragons) does not exist, since mating two heterozygotes would always result in the 1:2:1 ratio of purple to pink to white flowers.