Final answer:
The statement is false; a high genetic correlation typically indicates that two traits may be influenced by overlapping sets of genes, not that they do not share a gene.
Step-by-step explanation:
The statement "A high genetic correlation value indicates that two traits do not share a gene" is false. A high genetic correlation typically suggests that two traits are likely to be influenced by the same or by overlapping sets of genes. For instance, if there is a high genetic correlation between height and arm length, it may indicate that similar genetic factors affect both traits. This is consistent with Mendelian principles where the law of independent assortment states that genes do not influence each other with regard to the sorting of alleles into gametes; however, this principle applies when the genes are on different chromosomes or far apart on the same chromosome. When genes are close together on the same chromosome and do not undergo crossing over, they may be inherited together, which is an example of genetic linkage. An observed high genetic correlation can reflect such linkage or pleiotropy, where one gene influences multiple traits.