If you did not know the allele for purple flowers in pea plants was dominant to the allele for white flowers, how could you determine this experiemently?

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You would determine this the same way Mendel did.  Mendel bred a line of peas with purple flowers, and made sure that they did not get cross-pollinated with white-flowered plants.  He did the same thing with white-flowered plants taking care not to let them cross-pollinate with the purple flowers.  After several generations he had a purebred line of Purple flower peas (genotype PP), and a purebred line of white flower peas (genotype pp). You can get seeds for such purebreds from many plant nurseries nowadays. 

Then Mendel deliberately cross pollinated some of his purebreds.  Pollinating some white flowers with purple flower pollen, and pollinating some purple flowers with white flower pollen.  You can do the same thing.  Grow your peas until they bloom, cut off the pistils from each flower and insert them in the other color flower.  When the seeds from these cross-pollinated plants grow, they all have purple flowers, that means that purple flowers must be dominant to white flowers. 

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