Humans have yet another antigen system on their red blood cells. The MN blood group refers to a different antigen controlled by codominant alleles (MM, MN, and NN). A woman with blood types (O, MN, Rh+) had a baby with a man with the blood types (AB, N, Rh-). Unfortunately there was a mix up at the hospital, which of the following children belongs to the couple? And why?

a. Child #1: AB, N, Rh+
b. Child #2: A, M, Rh+
c. Child #3: A, MN, Rh-
d. Child #4: B, M, Rh+
e. Child #5: O, MN, Rh+
f. Child #6: O, MN, Rh-

I think it's child B or D but I'm not sure...

To determine which child belongs to the couple, we need to consider the blood type and the MN antigen system.

First, let's break down the blood types of the parents and the possible children:

Mother: O, MN, Rh+
Father: AB, N, Rh-
Possible Children:
a. Child #1: AB, N, Rh+
b. Child #2: A, M, Rh+
c. Child #3: A, MN, Rh-
d. Child #4: B, M, Rh+
e. Child #5: O, MN, Rh+
f. Child #6: O, MN, Rh-

Now let's analyze the possible combinations based on the inheritance patterns of blood types and the MN antigen system:

1. Blood type inheritance:
- The mother has blood type O, which means she can only pass on the O allele to her children.
- The father has blood type AB, meaning he can pass on either the A or B allele to his children.

Combining the blood types of the parents, we can eliminate options e and f since the father can't pass on the O allele.

2. MN antigen inheritance:
- The mother has the MN blood group, which means she can pass on either the M or N alleles to her children.
- The father has the N allele for the MN blood group.

Combining the MN antigen system of the parents, we can eliminate options c and d. In option b, the child has the M allele from the mother, which is incorrect since the mother only has MN antigen (MN = M and N).

Therefore, the child that belongs to the couple is:

a. Child #1: AB, N, Rh+

This is because Child #1 has the correct blood type inheritance (A and B alleles from the father) and does not have the M allele from the mother (as the mother only has MN antigen).

It's important to note that this analysis assumes that there are no other genetic factors at play and that the MN antigen system follows the expected patterns of inheritance.