Answer:
Jack parents' genotype = Both Heterozygous dominant (carrier)
Jack's genotype = could be homozygous dominant or heterozygous dominant
Jack and Jill can have a child with Tay-Sachs if both of them are heterozygous dominant for the disease.
Explanation:
Since Jack's brother died of the disease, his parents should be heterozygous dominant for the disease. Both the parents served as the carrier (Aa x Aa, assuming that allele "a" is responsible for Tay-Sachs disease) and had one affected child (Jack's bother= "aa").
Since Jack is not affected by the disease, he could be homozygous dominant (AA) or heterozygous dominant (Aa). But, his exact genotype could not be determined by the given information.
Child of Jack and Jill could be affected with the disease only if both of them are heterozygous dominant (Jack: Aa and Jill: Aa) and serve as the carrier for the disease.