1.Can a woman with A blood mate with a man with B blood and have children with O blood? 2.Which genes would the man and woman have in the example in the question above?

Yes

Explanation:

Yes, it is possible. If the woman would have blood AO and the father BO. This would mean there is a 25% chance the child could be OO blood. They would receive an O allele from their mom and an O allele from their dad, in all other cases the O allelle is recessive so AO would be A blood type and BO would be B blood type. AB would be type AB.

    B         O                                      

A   AB     AO                              

O   BO    OO                      

thats not even an aswer choice