Question

Let \( \mathbb{Z_8} \) = { 0,1,2,3,4,5,6,7,8} and \( \mathbb{Z_4} \) = {[0],[1],[2],[3]}. Define \( f: \mathbb{Z_8} --> \mathbb{Z_4}, g:\mathbb{Z_4} --> \mathbb{Z_8}, h:\mathbb{Z_8} --> \mathbb{Z_8}\) as follows: f(x)=[x+2], g([x])=2x and h(x)=2x+4

Answer 1

Let \( \mathbb{Z_8} \) = { 0,1,2,3,4,5,6,7,8} and \( \mathbb{Z_4} \) = {[0],[1],[2],[3]}. Define \( f: \mathbb{Z_8} --> \mathbb{Z_4}, g:\mathbb{Z_4} --> \mathbb{Z_8}, h:\mathbb{Z_8} --> \mathbb{Z_8}\) as follows: f(x)=[x+2], g([x])=2x and h(x)=2x+4 and f(x)=[x+2]

Answer 2

just so i could read it

Answer 3

Like all the numbers in \(\mathbb{Z_8} \) shld be having a line ontop if u know what i mean

Answer 4

looks like \(f\) is there twice

Answer 5

I guess it is looking for fog=h or something.

Answer 6

yeah that is ok, but it is not clear what the question is

Answer 7

just doing fog !

Answer 8

hahah yup i got so lost typing out all the extra info

Answer 9

also i am confused by \(\mathbb{Z_8}\)

Answer 10

g(f(x))=h(x)
so wld i have to show that its true for the 8 elements or whtvr

Answer 11

i think it should be \(\{0,1,2,3,4,5,6,7\}\)

Answer 12

and g(x)=[2x] , h(x)=[2x+4]

Answer 13

ans satelite right that is Z8

Answer 14

you can chase the diagram to do this, there are only a few elements to consider

Answer 15

i.e. you can write \(f,g,h\) as sets of ordered pairs

Answer 16

omfggggggggg u r right

Answer 17

i can write it if you like, but i am sure you can do it