A married couple with blood groups AB positive and O negative adopt a male child. Later, twin boys are born to them. The three sons have blood groups A positive, B positive, and O positive. What is the blood group of the adopted son?

Introduction / Context:
This question applies basic genetics of ABO blood groups and Rh factor to a family scenario. By using the possible genotypes of the parents, we can work out which blood groups their biological children can have and then deduce which child must be adopted. Such questions are popular in biology sections of competitive exams because they test reasoning, not just memorisation of blood group facts.

Given Data / Assumptions:

• Father's blood group: AB positive (genotype ABO: IAIB; Rh: Rh⁺, likely ++ or +-).
• Mother's blood group: O negative (genotype ABO: ii; Rh: Rh⁻, genotype --).
• Three sons have blood groups: A positive, B positive, and O positive.
• One son is adopted and two are biological twins; all are male, which does not affect ABO or Rh inheritance.

Concept / Approach:
For ABO inheritance, the father with AB has alleles IA and IB, and the mother with O has alleles i and i. Therefore, all biological children must inherit IA or IB from the father and i from the mother, giving genotypes IAi (group A) or IBi (group B). It is impossible for them to be group O (genotype ii) because neither parent can provide a second i allele. For the Rh factor, a positive father (+-) and negative mother (--) can have positive or negative children, but this does not change the ABO combinations. Thus, any biological child can only be A or B, never O, which identifies the adopted child.

Step-by-Step Solution:
Step 1: Determine possible ABO genotypes of biological children from AB (IAIB) × O (ii) parents. Step 2: Possible offspring genotypes are IAi (group A) or IBi (group B), because the child always gets i from the O parent and IA or IB from the AB parent. Step 3: Conclude that the biological children can only have blood groups A or B, not O or AB. Step 4: Examine the sons: A positive, B positive, and O positive. A and B are consistent with biological inheritance; O is not. Step 5: Therefore, the son with O positive blood group must be the adopted child.

Verification / Alternative check:
To further verify, we can look at the Rh factor. The father is positive (could be ++ or +-), and the mother is negative (--). A cross of +- × -- can produce +- (Rh positive) or -- (Rh negative) children. Thus, biological children may be Rh positive or negative. The question states that all sons are Rh positive, which is entirely possible for both adopted and biological children. However, the Rh data do not contradict the ABO conclusion that only A and B are biologically possible; O must therefore belong to the adopted son.

Why Other Options Are Wrong:
A positive: This can be a biological child since IAi (group A) is a valid genotype from AB × O parents. B positive: This can also be a biological child since IBi (group B) is possible from the same cross. Cannot be determined on the basis of the given data: Incorrect because the ABO inheritance clearly rules out O as a biological child in this parental combination. None of the above: Incorrect because O positive is a listed option and fits the adopted child logically.

Common Pitfalls:
Some students focus too much on the Rh factor and get confused, forgetting that ABO inheritance alone is enough to decide this question. Another common mistake is assuming that because the parents include group O, they can have a child with group O, ignoring the fact that the other parent is AB and cannot provide the second i allele needed to form ii. Carefully listing possible genotypes from the cross helps avoid such reasoning errors.

Final Answer:
The adopted son is the one with blood group O positive.