Thirty-three cities were researched to determine whether they had a professional sports team, a symphony, or a children's museum. Of these cities, 17 had a professional sports team, 14 had a symphony, 16 had a children's museum, 9 had a professional sports team and a symphony, 7 had a professional sports team and a children's museum, 7 had a symphony and a children's museum, and 4 had all three activities. Complete parts a) through e) below. a) How many of the cities surveyed had only a professional sports team? 5 (Simplify your answer.) b) How many of the cities surveyed had a professional sports team and a symphony, but not a children's museum? 5 (Simplify your answer.) c) How many of the cities surveyed had a professional sports team or a symphony? (Simplify your answer.)

Step 1 ：Calculate the number of cities that had only a professional sports team by subtracting the number of cities that had a professional sports team and a symphony, and the number of cities that had a professional sports team and a children's museum, from the total number of cities that had a professional sports team. Then add back the cities that had all three activities. The calculation is: \(17 - 9 - 7 + 4 = \boxed{5}\) cities.

Step 2 ：Calculate the number of cities that had a professional sports team and a symphony, but not a children's museum, by subtracting the number of cities that had all three activities from the number of cities that had a professional sports team and a symphony. The calculation is: \(9 - 4 = \boxed{5}\) cities.

Step 3 ：Calculate the number of cities that had a professional sports team or a symphony by adding the number of cities that had a professional sports team and the number of cities that had a symphony. Then subtract the cities that had both. The calculation is: \(17 + 14 - 9 = \boxed{22}\) cities.