Final answer:
Different gene pairs on the same homologous chromosomes (if far apart) or on nonhomologous chromosomes do separate independently during meiosis due to the process of independent assortment and recombination as a result of crossing-over.
Step-by-step explanation:
The question addresses whether different gene pairs on the same homologous chromosomes or on nonhomologous chromosomes separate independently from each other during meiosis. The process governing this is known as Mendel's law of independent assortment, which states that genes sort independently of each other into gametes. This is because chromosomes, and therefore the genes on them, assort independently during meiosis. Recombination during crossing-over ensures that even genes on the same chromosome can often be inherited independently, especially if they are far apart. Crossing-over is more likely to separate alleles of genes that are far apart on the same chromosome, leading to independent assortment.
Therefore, the correct option is: 1) Yes. Different gene pairs on the same homologous pair of chromosomes, if they are far apart, or on nonhomologous chromosomes do indeed separate independently from each other during meiosis, due to the process of independent assortment and crossing-over.