Correct Option
The blood group of the couple is AB positive and O negative. In the ABO blood group system, the parent with AB blood group has genotype IᴬIᴮ, and the parent with O blood group has genotype ii. Their biological offspring can inherit either the Iᴬ allele or the Iᴮ allele from the AB parent and the i allele from the O parent. Thus, their biological children can only have genotypes Iᴬi (Blood Group A) or Iᴮi (Blood Group B). They cannot have Blood Group O (genotype ii).
The problem states that the couple had twin boys with blood groups A positive and B positive. These blood groups are genetically possible for their biological children (Iᴬi and Iᴮi, respectively, with Rh positive factor inherited from the AB positive parent). The third son has blood group O positive. Since Blood Group O is not a possible blood group for the biological offspring of a couple with AB and O blood groups, the son with O positive blood group must be the adopted child.
Incorrect Options
Options 2 (A positive) and 3 (B positive) represent the blood groups of the biological twin sons born to the couple, not the adopted son.
Option 4 (Cannot be determined on the basis of the given data) is incorrect because, through genetic analysis of blood group inheritance, the blood group of the adopted son can be definitively identified by eliminating the genetically possible blood groups for the biological children.