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
Let where , and , is hour of clock and is minute of digital clock.
a. Let us show that is not well defined. Indead, if we consider and , that is the hours , we have that maps to at least two values and Therefore, is not well defined.
b. Let us show that is not a one-to-one correspondence. Indeed, if we consider and , that is the hours , we have that and map to the same value Therefore, is not a one-to-one correspondence.
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