Q52
For all non-negative integers x and y, f(x, y) is defined as below
f(0, y) = y + 1
f(x + 1, 0) = f(x, 1)
f(x + 1,y + 1) = f(x, f(x + 1, y))
Then, what is the value of f(1, 2)?
Answer: B
f (1, 2) = f(0 + 1, 1 + 1) = f(0, f(0 + 1, 1)) = f(0, f (1, 1))
f (1, 1) = f(0, f(1, 0))
f(1, 0) = f(0, 1) = 2
∴ f(1, 1) = f(0, 2) = 2 + 1 = 3
f (1, 2) = f(0 + 1, 1 + 1) = f(0, f(0 + 1, 1)) = f(0, f (1, 1)) = f(0, 3)
f(0, 3) = 3 + 1 = 4
Hence, option (b).