Exercise 17.5.19. (a) Show that absolute value does not produce a well-defined function from Z7 to Z7. That is, show there exist a, b = Z, such that [a]7 = [b]7, but [la]]7 # [1³] 7. (b) Show that part (a) is true for every n>2. That is, show that absolute value does not provide a well-defined function from Zn to Zn-

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Please do Exercise 17.5.19  part A and B and please show step by step and explain

Exercise 17.5.19.
(a) Show that absolute value does not produce a well-defined function from Z7
to Z7. That is, show there exist a, b = Z, such that
[a]7 = [b]7, but [la]7 ‡ [16]] 7.
(b) Show that part (a) is true for every n > 2. That is, show that absolute
value does not provide a well-defined function from Zn to Zn.
Transcribed Image Text:Exercise 17.5.19. (a) Show that absolute value does not produce a well-defined function from Z7 to Z7. That is, show there exist a, b = Z, such that [a]7 = [b]7, but [la]7 ‡ [16]] 7. (b) Show that part (a) is true for every n > 2. That is, show that absolute value does not provide a well-defined function from Zn to Zn.
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