Final answer:
If genes are completely linked, all the progeny will have the phenotype of one parent. If genes are unlinked and able to independently assort, it is false that all the progeny will only have the phenotype of one parent.
Step-by-step explanation:
No, the statement is false. If genes are completely linked, it means that they are located very close together on the same chromosome and do not undergo crossing over during meiosis. In this case, the genes are inherited together and all the offspring will have the phenotype of one parent.
On the other hand, if genes are unlinked and are able to independently assort, it means that they are located on different chromosomes or are far apart on the same chromosome. In this case, crossing over can occur and there is a chance for recombination, resulting in offspring that have a combination of traits from both parents.