recursive definition. Consider the following inductive definition of a version Links of Ackermann's function. This function was named after Wilhelm Ackermann, a German mathematician who was a student of the great mathematician David Hilbert. Acker- mann's function plays an important role in the theory of re- cursive functions and in the study of the complexity of certain algorithms involving set unions. (There are several different variants of this function. All are called Ackermann's function and have similar properties even though their values do not always agree.) 2n if m = 0 0 if m > 1 and n = 0 A(m, n) : 2 if m > 1 and n = 1 A(m - 1, A(m, n - 1)) ifm > 1 and n 2 250. Find these values of Ackermann's function. a) A(1, 0) b) A(0, 1) c) A(1, 1) d) A(2, 2) 51. Show that A(m, 2) = 4 whenever m > 1. 52. Show that A(1, n) = 2" whenever n > 1. 53. Find these values of Ackermann's function. a) A(2, 3) *b) A(3, 3) #54. Find A(3, 4). #55. Prove that A(m, n + 1) > A(m, n) whenever m and n are nonnegative integers. #56. Prove that A(m + 1, n) 2 A(m, n) whenever m and n are nonnegative integers