The first filial (#"F"_1"#) generation is the result of a cross between the parental (#"P"#) generation. In Mendel's study of heredity in pea plants, the parental generation in the cross would be two true-breeding (homozygous) plants that differ in a particular trait; for example tall or short plants, and purple or white flowers.The purpose of the cross is to analyze the pattern of inheritance for a particular trait.