If the father in a family has a disease while the mother is normal, the daughters only are inherited by this disease and not the sons. Name this type of disease?

The correct option is Sex-linked dominant.

Let us break down the inheritance pattern step-by-step to understand why this type of disease is sex-linked dominant:
1. Understanding Sex Chromosomes: Humans have a pair of sex chromosomes that determine biological sex. Females have two X chromosomes ($XX$), while males have one X and one Y chromosome ($XY$).
2. Parental Genotypes:
- The mother is unaffected ("normal"). Since she is a female, she has two normal X chromosomes ($X^d{X}^d$, where $X^d$ represents the normal allele).
- The father is affected by the disease. Since he is a male, he has one X chromosome and one Y chromosome. For a sex-linked disease, the gene is located on the sex chromosome. Since it is passed specifically from the father to all of his daughters but none of his sons, the disease-causing gene must reside on the X chromosome. Therefore, his genotype is $X^{D}Y$ (where $X^D$ represents the mutant, disease-causing allele).
3. Inheritance by Offspring:
- Sons: A father passes his Y chromosome to all of his sons, while the mother passes one of her X chromosomes. Since the sons receive the Y chromosome from the affected father and a normal X chromosome ($X^d$) from the mother, their genotype is $X^{d}Y$. Consequently, none of the sons inherit the disease.
- Daughters: A father passes his single X chromosome ($X^D$) to all of his daughters, while the mother passes one of her normal X chromosomes ($X^d$). Therefore, all daughters inherit the mutant X chromosome from their father, resulting in the genotype $X^D{X}^d$.
4. Dominant vs. Recessive: Since the daughters have one disease-causing allele ($X^D$) and one normal allele ($X^d$) but still express the disease, the disease-causing allele must be dominant. If the disease were sex-linked recessive, the daughters would only be carriers and would not show the disease because they have a normal X chromosome from their mother.
Thus, the inheritance pattern where an affected father passes the trait to all of his daughters and none of his sons is characteristic of a Sex-linked dominant disease.