ANSWER -
The disease that the woman's sons, but not her daughters, inherit is Hemophilia, a genetic bleeding disorder caused by a deficiency or dysfunction of certain blood clotting factors. Hemophilia is an X-linked recessive disorder, which means that the gene responsible for the disease is located on the X chromosome and is inherited in a pattern of X-linked recessive inheritance.
A woman who is heterozygous for the recessive hemophilia gene (carrying one normal and one abnormal gene) does not exhibit the disease because the normal gene compensates for the abnormal gene. However, she can pass on the abnormal gene to her offspring.
If a woman who is heterozygous for the hemophilia gene has children with a man who does not have the disease, her daughters will have a 50% chance of inheriting the normal gene from her, and her sons will have a 50% chance of inheriting the abnormal gene from her. As a result, her daughters will not exhibit the disease, but her sons will exhibit the disease if they inherit the abnormal gene.