In AB, B takes 1 to 3, and A will take 3 to 7, so 1 -> 7 (remember, A and B are essentially functions on their domains). In B, 2 goes to 5, and in A 5 goes to 4, so 2 ->4 is the new rule. In summary, 1->7, 2->4, 3 -> 6, 4 -> 3, 5 -> 1, 6 -> 5, 7 -> 2, 8 -> 9, 9 -> 8 (since 8 cycles to itself in A). Now, putting this all together, begin with any number, like 1, and follow the trail until you've returned to 1 again. (1724365)(89) is the new composed rule AB. Your turn for BA.