Final answer:
The mother must carry at least one A allele to express the A protein. The father's genotype must be B/B as he expresses the B protein and his daughter exhibits the B protein due to maternal imprinting. option c is correct.
Step-by-step explanation:
In this scenario, an autosomal gene with maternal imprinting determines the presence of different forms of blood protein, and there are alleles A and B. For their daughter to express only the B protein and their son to express only the A protein, despite their mother having only A protein and their father having only B protein, we need to consider the mechanics of imprinting and inheritance in autosomal genes. Since imprinting involves the silencing of one parental allele, we can deduce the following about the parents' genotypes:
Mom has at least one A allele. This is clear because she expresses only the A protein.
Dad must have at least one B allele, as he expresses only the B protein.
The fact that the daughter expresses only the B protein suggests that the expressed allele comes from the father, and the mother's allele is imprinted (silenced).
The son's expression of only the A protein indicates the father's allele is imprinted, and the mother's A allele is expressed.
Considering these points:
Mom's genotype could be A/A or A/B. Since the A allele from the mother is imprinted in the daughter, the B allele must come from her father, suggesting that he is heterozygous A/B or homozygous B/B, but we know he expresses only the B protein, so he must have at least one B allele.
Dad's genotype must be B/B, as he expresses only the B protein and the son has A protein, which indicates that the son inherited a silenced B allele from the father and an active A allele from the mother.