Final answer:
A man with type AB blood (genotype IAIB) cannot be the father of a child with type O blood (genotype ii), as he cannot provide the recessive i allele required for the child's blood type.
Step-by-step explanation:
The question is focused on the inheritance of ABO blood types and whether a man with AB blood type could be the father of a child with type O blood. Given that a woman with heterozygous type A blood (genotype AO) has a child with type O blood (genotype ii), if the man claimed to be the father has type AB blood (genotype IAIB), he cannot be the biological father of the child because he would pass either an IA or an IB allele to the child, not the required i allele for type O blood.
In the scenario where one parent is genotype AO and the other parent is genotype BO, their offspring could indeed have any of the four blood types: A (genotype AO or IAIA), B (genotype BO or IBIB), AB (genotype IAIB), or O (genotype ii). However, a parent with genotype IAIB (type AB blood) cannot have a child with type O blood because they do not possess the i allele necessary to produce the genotype ii.