To solve this problem, we need to determine the possible blood groups of the offspring when a man with blood group 'A' marries a woman with blood group 'B'.$\newline$Blood group inheritance is determined by the alleles:$\newline \bullet$IA (A allele), IB (B allele), and i (O allele).$\newline$The possible genotypes for blood group 'A' are IAIA and IAi.$\newline$The possible genotypes for blood group 'B' are IBIB and IBi.$\newline$Let's consider the combinations:$\newline \bullet$If the man is IAIA and the woman is IBIB, the offspring can only be IAIB (blood group AB).$\newline \bullet$If the man is IAIA and the woman is IBi, the offspring can be IAIB (blood group AB) or IAi (blood group A).$\newline \bullet$If the man is IAi and the woman is IBIB, the offspring can be IAIB (blood group AB) or IBi (blood group B).$\newline \bullet$If the man is IAi and the woman is IBi, the offspring can be IAIB (blood group AB), IAi (blood group A), IBi (blood group B), or ii (blood group O).$\newline$Therefore, the possible blood groups of their offspring are A, B, AB, and O.$\newline$This corresponds to Option 3.