Show that each of these proposed recursive definitions of
Chapter 5, Problem 59E(choose chapter or problem)
Problem 59E
Show that each of these proposed recursive definitions of a function on the set of positive integers does not produce a well-defined function.
a) F(n) = 1 + F([(n + 1)/2]) for n ≥ 1 and F(1) = 1.
b) F(n) = 1 + F(n - 2) for n ≥2 and F(l) = 0.
c) F(n) = 1 + F(n/3) for n ≥ 3, F(l) = 1, F(2) = 2, and F(3) = 3.
d) F(n) = 1 + F(n/2) if n is even and n ≥ 2,F(n) = 1 + F(n - 2) if n is odd, and F(l) = 1.
e) F(n) = 1 + F(F(n - 1)) if n ≥ 2 and F(l) = 2.
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