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Gregor Mendel performed a series of experiments on pea plants to understand how traits are passed on from one generation to the next. In his monohybrid cross experiments, Mendel crossed pea plants that had contrasting traits for one characteristic, such as seed color (yellow or green). He then observed the traits in the resulting offspring and noticed a pattern in their inheritance.

Based on his monohybrid cross experiments, Mendel developed four postulates, which laid the foundation for the modern science of genetics. The postulates are as follows: 1. The Law of Segregation: Each organism has two alleles for a trait, and these alleles separate during the formation of gametes so that each gamete carries only one allele for a trait. 2. The Law of Dominance: In a pair of contrasting alleles, one allele is dominant, and the other is recessive. The dominant allele determines the organism's appearance, while the recessive allele has no effect on the organism's appearance. 3. The Law of Independent Assortment: Genes for different traits are inherited independently of each other during the formation of gametes. 4. The Law of Unit Characteristics: Each trait is determined by a pair of genes; one gene comes from the mother and one from the father.

Based on our understanding of Mendel's monohybrid results and his postulates, we can determine that the third postulate, the Law of Independent Assortment, was not based on these results.

The Law of Independent Assortment was not based on monohybrid results because it concerns the inheritance of genes for two or more traits, rather than inheritance of just one trait as observed in the monohybrid experiments. Mendel derived this postulate from another set of experiments, known as dihybrid crosses, in which he crossed pea plants that had contrasting traits for two characteristics, such as seed color and seed shape. By studying the inheritance patterns of these two traits, Mendel concluded that the genes for different traits were inherited independently of each other.