Hairlessness in American rat terriers is recessive to the presence of hair. Suppose that you have a rat terrier with hair. Explain how can you determine whether this dog is homozygous or heterozygous for the hairy trait by setting up a mating.

By performing a test cross i.e. a cross with a recessive trait

Explanation:

According to the question, hairlessness is a recessive trait, meaning that it will only be expressed in a homozygous condition i.e. when there are two recessive alleles in the genotype. Presence of hair is dominant, meaning that it will mask the phenotypic expression of hairlessness allele in a heterozygous state. Hence, a dominant phenotype can either be homozygous (same dominant allele) or heterozygous (combination of dominant and recessive alleles).

In order to determine which of these genotypes the dominant phenotype possess, we perform a test cross. A test cross is a cross performed to determine the genotype of the dominant organism by crossing it with a homozygous recessive genotype.

Ideally, the offsprings resulting from the cross will all be phenotypically dominant if the organism in question is homozygous dominant but if the organism is heterozygous dominant, the offsprings will occur in an equal ratio of dominant to recessive phenotypes.

So in this case, all of offsprings of this cross between the rat terriers will possess hair if the dominant rat terrier dog is homozygous, but if the dominant rat terrier dog is heterozygous, an hairless offspring will be produced.