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(a) Show that ct : Z3 -+ Z6 given by ct([ah) = [a]6 is not well defined. (Compare

Chapter 21, Problem 21.6

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QUESTION:

(a) Show that ct : Z3 -+ Z6 given by ct([ah) = [a]6 is not well defined. (Compare 21.5.)(b) For which pairs m, n is f3 : Zm -+ Zn defined by f3([a]m) = [a]" well defined?

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QUESTION:

(a) Show that ct : Z3 -+ Z6 given by ct([ah) = [a]6 is not well defined. (Compare 21.5.)(b) For which pairs m, n is f3 : Zm -+ Zn defined by f3([a]m) = [a]" well defined?

ANSWER:

Step 1 of 2

Show that   by  is not well defined.

(a) is well defined.

First, note that  is well defined function, since if  in, then  and this implies that  (from the data)

And also, which is wrong.

Hence the mapping  by  is not well – defined.

 

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