Discuss the below:
Q: Suppose that X and Y are finite sets, with m and n elements respectively. Suppose further that the function f : X → Y is one-to-one and the function g : X →Y is onto.
(i) Use the function f to show that m ≤ n.
(ii) Use the function g to show that m ≥ n.
(iii) Is f : X → Y onto? Justify your assertion.
(iv) Is the function g : X → Y one-to-one? Justify your assertion.