Final answer:
By comparing elements of sets A and B, we figure out that a=3. There are no further restrictions on b apart from it not resulting in any element in A when added to a. Therefore, the final intersection A AND B is {4,7}.
Step-by-step explanation:
Given sets A = {3,7,a2} and B = {2,4,a+1,a+b}, and the intersection A AND B = {4,7}, we begin by comparing the elements of A and B to identify common elements, which are the intersection. Since 7 is in both A and B, we don't have any restrictions on a or b from this number. However, 4 is only present in set B, suggesting that a has to be 3 since a+1=4, thus a=3. Now, set A will be {3,7,9} with a=3. There are no other common elements in sets A and B, so for any b, a+b should not equal to any element in set A excluding 4; b can be any integer except -2 (because a-2=1 which is not in set A) and -5 (because a-5=3 which is already in set A as a2=9).
To find the intersection A AND B, we list the elements after assuming a=3, which gives us A = {3,7,9}. Since B includes 4 and other values dependent on b, none of which are 3, 7, or 9, the final intersection remains A AND B = {4,7}.