a garden pea plant bearing terminal violet flowers when crossed with another pea plant axial violet flowers produce axial, violet, axial white flowers in the ratio 3:1 . work out the cross showung the genotype of the parent plantand their progeny . name the law

The given scenario describes a cross between a garden pea plant with terminal violet flowers (TTVV) and another pea plant with axial violet flowers (ttvv). When these two plants are crossed, their offspring have axial violet flowers in a ratio of 3:1 (AxV:AxW).

To determine the genotypes of the parent plants, we need to use the information provided. Based on the offspring's phenotypes and ratios, we can deduce the genotypes of the parent plants.

Let's use the following symbols:
- T: Dominant allele for terminal flowers
- t: Recessive allele for axial flowers
- V: Dominant allele for violet flowers
- v: Recessive allele for white flowers

The first parent plant has the genotype of TTVV (terminal violet flowers), as mentioned in the question. The second parent plant, which has axial violet flowers, must have the genotype ttxx (axial flowers, where the "x" represents either violet or white color).

To work out the cross, we can represent the genotypes of the parents:

First parent (P1): TTVV
Second parent (P2): ttxx

To determine the genotype of the progeny (offspring), we need to conduct a Punnett square analysis. Let's fill the Punnett square using the genotypes of the parents:

T T V V
t t | Tt | Tt | Vv | Vv
t x | Tt | Tt | Vx | Vx

From the Punnett square, we can observe that all the progeny have the genotype TtVv, giving them axial violet flowers. This corresponds to the ratio of 3:1 mentioned in the question.

The Law associated with this scenario is Mendel's Law of Independent Assortment. According to this law, alleles for different traits segregate independently of one another during the formation of gametes.