Final answer:
A man with blood type A and a woman with blood type B could never produce a child with blood type AB if both are homozygous with genotypes AA and BB respectively. If one or both parents is heterozygous, they can have a child with any ABO blood type, including AB.
Step-by-step explanation:
A man with blood type A and a woman with blood type B could never produce a child with blood type AB only if both are homozygous for their respective blood type alleles (meaning the man has genotype AA and the woman has genotype BB). The ABO blood types are determined by the presence or absence of two antigens, A and B, on the surface of red blood cells. An individual with type A blood has A antigens on their red blood cells and produces anti-B antibodies, while an individual with type B blood has B antigens and produces anti-A antibodies. Blood type O individuals lack both antigens and produce both types of antibodies.
An individual with blood type O (genotype ii) could legitimately be a child of one parent with blood type A and another with blood type B if both parents are heterozygous (genotype Ai and Bi, respectively). In this scenario, each parent contributes the i allele, resulting in a child with type O blood.
Therefore, if a man with genotype AA and a woman with genotype BB have children, the children cannot have blood type O or AB since the O and AB types would require at least one i allele from either parent, which they do not have. However, if one or both parents are heterozygous (Ai, Bi), they could produce a child with any of the four blood types A, B, AB, or O.