Given sets A, B, we define a partial function f with domain A and codomain B as a function from Af to B, where ϕ ≠ A'⊂ A. [Here f(x) is not defined for x ∈ A - A'.] For example, f : R* → R, where f(x) = 1/x, is a partial function on R since f(x) is not defined. On the finite side, {(1, x), (2, k), (3, y)} is a partial function for domain A = {1,2, 3,4, 5} and codomain B = {w, x, y, z}. Furthermore, a computer program may be thought of as a partial function. The program's input is the input for the partial function and the program's output is the output of the function. Should the program fail to terminate, or terminate abnormally (perhaps, because of an attempt to divide by 0), then the partial function is considered to be undefined for that input, (a) For A = {1, 2, 3, 4, 5}, B = {w, x, y, z}, how many partial functions have domain A and codomain B? (b) Let A, B be sets where |A| = m > 0, |B| = n > 0. How many partial functions have domain A and codomain B?