Assignment:
Let f:N x N -> N be the function defined recursively as follows:
f(0, 0) = 6
f(i, j) = f(i - 1, j) + 2 if i > 0 and j = 0
f(i, j) = f(i, j - 1) + 1 if j > 0
Use induction on the sum i + j to prove that f(i, j) = 2i + j + 6 for all (i, j) in N x N.
Provide complete and step by step solution for the question and show calculations and use formulas.