i got the final answers of..
X = {xͼA | All real numbers }
Y = {yͼA | -sqrt(5k) >= y sqrt(5k), For some integer of k}
dunno if that is correct..
Define the equivalence relation S by S = {(x,y)ͼAxA | 5 divides (x^2-y^2)}.
Determine the partition of A that is induced by S.
I am not exactly sure how to do this one but from what I gather from my textbook it seems to sorta start like this..
Given
Am I doing this correctly? On the right track?
Hello KitizhiAre you familiar with the modulo notation, to show the remainder when one integer is divided by another? If is a multiple of , then
Now look at the various possible values of , for :
So
And
Do you understand the notation I've used here? Can you complete it, starting with and then using this to describe the equivalence classes?
Grandad