Question #165322

 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 


1
Expert's answer
2021-02-24T07:49:44-0500

Let f:XYf:X\to Y where x,yZ+x, y\in \mathbb Z^+, and 0x23,0y590\le x\le 23, 0\le y\le 59, xx is hour of clock and yy is minute of digital clock.


a.     Let us show that f:XYf:X→Y is not well defined. Indead, if we consider x=1x=1 and y1=10, y2=20y_1=10,\ y_2=20, that is the hours 1:10, 1:201:10,\ 1:20, we have that x=1x=1 maps to at least two values y=10y=10 and y=20.y=20. Therefore, f:XYf:X→Y is not well defined.


b.   Let us show that f:XYf:X→Y is not a one-to-one correspondence. Indeed, if we consider x1=1x_1=1 and x2=2, y1=y2=20x_2=2,\ y_1=y_2=20, that is the hours 1:20, 2:201:20,\ 2:20, we have that x1=1x_1=1 and x2=2x_2=2 map to the same value y=20.y=20. Therefore, f:XYf:X→Y is not a one-to-one correspondence.



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