Question

 A f:X→Y where X,Y ∈ Z+ , and 0≥ X ≤23 and, 0≥ Y≤59, X is hour of clock and Y is minute of digital clock, Proof the following

a. Is f:X→Y is well defined?

b. Is f:X→Y a one-to-one correspondence

Answer 1

The function f:X→Y is not well defined, because of domain and codomain of a function (or a map) must be sets. But from the text "X,Y ∈ Z+ , and 0≥ X ≤23 and, 0≥ Y≤59, X is hour of clock and Y is minute of digital clock" one may conclude that X,Y are integers or variables, not sets.

The question "Is f:X→Y a one-to-one correspondence", therefore, doesn't make any sense.