A fair die is rolled twice. Let \(A\) be the event that the number on the first die is odd, let \(B\) be the event that the number on the second die is odd, and let \(C\) be the event that the sum of the two rolls is equal to 7.

a. Show that \(A\) and \(B\) are independent, \(A\) and \(C\) are independent, and \(B\) and \(C\) are independent. This property is known as pairwise independence.

b. Show that \(A, B\), and \(C\) are not independent. Conclude that it is possible for a set of events to be pairwise independent but not independent.