A man with blood group 'A'  marries a woman with blood group 'B'.  What are all the  possible blood  groups of their offspring?

A man with blood group A marries a woman with blood group B. 

The genotype of the man may be ${\text{I}}^{\mathrm{A}}{\mathrm{I}}^{\mathrm{A}}or {\mathrm{I}}^{\mathrm{A}}\mathrm{i}$

The genotype of the woman can be ${\text{I}}^{\mathrm{B}}{\mathrm{I}}^{\mathrm{B}}or {\mathrm{I}}^{\mathrm{B}}\mathrm{i}$

If the man has genotype ${\text{I}}^{\mathrm{A}}{\mathrm{I}}^{\mathrm{A}}$ and woman has genotype ${\text{I}}^{\mathrm{B}}{\mathrm{I}}^{\mathrm{B}}$ then all the offspring produced will have genotype of ${\text{I}}^{\mathrm{A}}{\mathrm{I}}^{\mathrm{B}}$. But we no such options. 

Therefore, we will assume that the genotype of man is ${\text{I}}^{\mathrm{A}}\mathrm{i}$ and the genotype of woman is ${\text{I}}^{\mathrm{B}}\mathrm{i}$.

${\text{I}}^{\mathrm{A}}\mathrm{i}$ X ${\text{I}}^{\mathrm{B}}\mathrm{i}$.

Gametes of man is: ${\text{I}}^{\mathrm{A}}$ and i

Gametes of woman is: ${\text{I}}^{\mathrm{B}}$ and i

The genotypes of the offspring are ${\text{I}}^{\mathrm{A}}{\mathrm{I}}^{\mathrm{B}}$, ${\text{I}}^{\mathrm{A}}\mathrm{i}$, ${\text{I}}^{\mathrm{B}}\mathrm{i}$ and ii