Exercise 17.1.16 Apply the reflection principle repetitively to verify that

|Ai| =







n n+a+b+(i−1) s 2



for odd i



n n+a−b+is 2



for even i

, |Bi| =







n n−a−b+(i+1) s 2



for odd i



n n−a+b+is 2



for even i

.

Assume that n+a−b is even for |Ai | and n−a+b is even for |Bi |.