Final answer:
True-breeding purple-stemmed plants will only produce offspring with purple stems when interbred. This is due to the homozygous nature of pure breeding populations resulting in a consistent phenotype. Mendel's experiments illustrated similar principles through the inheritance of flower colors in pea plants.
Step-by-step explanation:
If plants from a pure breeding population of purple-stemmed plants interbreed with plants within that population, they will only give rise to purple-stemmed plants. This statement is True. A pure breeding, or true breeding, population implies that the plants have homozygous alleles for particular traits, in this case, the purple stem color. When these plants interbreed, or self-pollinate, all their offspring would express the same phenotype for stem color as they inherit the same genetic information for that trait.
Gregor Mendel's classic experiments with pea plants demonstrated the principles of inheritance. When he crossed plants that were true-breeding for violet flower color with plants true-breeding for white flower color (the P generation), all the resulting hybrids in the F1 generation had violet flowers, displaying a dominant trait. In the F2 generation, which resulted from the self-fertilization of the F1 hybrids, approximately three-quarters of the plants had violet flowers, and one-quarter had white flowers, indicating the reappearance of the recessive trait.
Therefore, a cross involving only purple-stemmed plants from a true-breeding population will yield offspring with the same purple-stemmed characteristic. However, if traits for stem length or flower color are also considered, the outcome might be different, depending on whether these traits are linked to stem color and on their dominant or recessive status.