Solution to A f:X→Y where X,Y ∈ Z+ , and 0≤ X ≤23 and, 0≤Y≤59, X is … - Sikademy
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Archangel Macsika

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

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Let f:X\to Y where x, y\in \mathbb Z^+, and 0\le x\le 23, 0\le y\le 59x is hour of clock and y is minute of digital clock.

a.     Let us show that f:X→Y is not well defined. Indead, if we consider x=1 and y_1=10,\ y_2=20, that is the hours 1:10,\ 1:20, we have that x=1 maps to at least two values y=10 and y=20. Therefore, f:X→Y is not well defined.

b.   Let us show that f:X→Y is not a one-to-one correspondence. Indeed, if we consider x_1=1 and x_2=2,\ y_1=y_2=20, that is the hours 1:20,\ 2:20, we have that x_1=1 and x_2=2 map to the same value y=20. Therefore, f:X→Y is not a one-to-one correspondence.

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