In Example 39, prove the following facts, where C(n) = the total number of nodes in the
Chapter 4, Problem 72(choose chapter or problem)
In Example 39, prove the following facts, where C(n) = the total number of nodes in the decision tree at level n, H(n) = the total number of nodes at level n resulting from an H toss, T(n) = the total number of nodes at level n resulting from a T toss.\(^1\)
a. C(n) = H(n) + T(n)
b. H(n) = T(n − 1)
c. T(n) = H(n − 1) + T(n − 1)
d. H(n) = H(n − 2) + T(n − 2)
e. C(n) = C(n − 2) + C(n − 1) for \(n \geq 3\)
f. C(n) = F(n + 1) where F(n) is the nth Fibonacci number
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