Question

Let \( \mathbb{Z_4} \) = {[0],[1],[2],[3]} Define k:\( \mathbb{Z_4} \) ---> \( \mathbb{Z_4} \) as follows: k([x])=[2x+2]
By comparing images verify the following equality
k(k(x)) = [2] for all x in \( \mathbb{Z_4} \)

Answer 1

which inequality?

Answer 2

sorry equality

Answer 3

What course is this? Discrete Math?

Answer 4

nope but smth similar

Answer 5

What is the name of your course?

Answer 6

@KingGeorge can u check this out? Like I have an answer but it isnt soo formal

Answer 7

What's your answer you have so far?

Answer 8

k(k(x)) = k(2x+2)=4x+6
Since k is a function in \( \mathbb{Z_4} \) then by mod 4, 4x+6-y=4k for some integer y and k
4x+6-2=4k
4x+4=4
4(x+1)=4k
Since 4 divides 4x+6 therefore 4x+6=2mod4. Hence 4x+6 is in teh equivalence class [2]

Answer 9

idk like its just a guess. I wasnt sure what i was exactly supposed to show

Answer 10

That works, but I don't think it's exactly how they were intending you to show it.

I think they meant for you to look at \[k(k([0]))\]\[k(k([1]))\]\[k(k([2]))\]\[k(k([3]))\]individually, and then verify that they all equal \([2]\).

Answer 11

ohhhhhhhhhhhhhhhhhh

Answer 12

y cant i ever figure out what to doooo?

Answer 13

Probably because the problems aren't worded spectacularly well.

Answer 14

Thanks KGGGGGGG

Answer 15

You're welcome.

Answer 16

waiittt can u show me how u wld plug it in?

Answer 17

Let's use [1] for an example. \[k(k([1]))=k([2\cdot1+2])=k([4])=k([0])=[2\cdot0+2]=2\]

Answer 18

ohhhh i seeeee

Answer 19

so lets sat k(k([0]))=k([2*0+2])=k([2])=[2*2+2]=[6]=[2]

Answer 20

Right.

Answer 21

yayyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

Answer 22

Thankkkss uuuuuu veryyy much for saving my soul

Answer 23

lol :P You're welcome.