Define a function A: N x N -> N as follows: A(m, n) ={2n, if m= 0; 0, if m≥1 and n= 0; 2, if m≥1 and n= 1; A(m-1, A(m, n-1)), if m≥1 and n≥2 (a) Calculate the following: (i)A(1,0) (ii)A(0,1) (iii)A(1,1) (iv)A(2,2).
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Consider the function
(i) Since and we use the formula , and have that
(ii) Since we use the formula , and have that
(iii) Since and we use the formula , and have that
(iv) We use the formula for and to conclude that .
In the following we use the formula to calculate and , and the formula to calculate