is this statement correct c) The male offspring of the mother will have 50% will manifest the disease, and the female offspring will be the carriers of the disease with 50%.

The correctness of the statement depends on the context, specifically the type of genetic inheritance pattern the disease follows.

If the disease is X-linked recessive, then the statement is partially correct. Male offspring who receive the affected X chromosome from their mother will indeed manifest the disease, because males have only one X chromosome. However, the percentage will depend on the father's genotype. If the father is healthy, then yes, 50% of the male offspring will manifest the disease (those who receive the mother's affected X chromosome), and 50% will be healthy (those who receive the mother's healthy X chromosome).

For the female offspring, they will be carriers if they inherit one affected X chromosome from the mother and one healthy X chromosome from the father. However, if they inherit the affected X chromosome from both parents, they will manifest the disease. So, it's not always true that 50% of the female offspring will be carriers. The percentage can vary depending on the father's genotype.

If the disease follows a different pattern of genetic inheritance (like autosomal dominant or autosomal recessive), then the statement would not be correct.

So, without additional context about the disease and the parents' genotypes, it's not possible to definitively say whether the statement is correct or not.