Final answer:
The Law of Independent Assortment is not supported in a dihybrid cross where pink flowers only occur with small petals and white flowers with large petals. This suggests that the genes for flower color and petal size may not segregate independently due to linkage. The Law of Segregation is supported as traits appeared in a near 3:1 ratio in the F2 generation.
Step-by-step explanation:
When a dihybrid cross is performed on pea plants for flower petal size and color, and the observable traits are found to be close to a 9:3:3:1 phenotypic ratio, but pink flowers only appear with small petals while white flowers appear with large petals, it indicates that the Law of Independent Assortment is not supported. The Law of Segregation is supported as each gene segregates independently during gamete formation, and the traits appear in a near 3:1 ratio in the F2 generation, as observed by Mendel.
The key issue here is that pink flowers are not appearing independently of petal size, which suggests that the two traits are linked in some way and do not assort independently. This violates Mendel's law of independent assortment, which predicts that each pair of alleles segregates independently of any other pair and combines randomly. The evidence of a non-random association between flower color and petal size suggests that the genes influencing these traits might be located close together on the same chromosome or might be influenced by the same genetic factors, and therefore cannot assort independently.