Answer:
[1]=Z the set of integers
[1/2]={r/2| r is an odd integer}
Step-by-step explanation:
Denote by [a] the equivalence class of an element a.
We know that [a]={x|(x,a)∈R}. Then
[1]={x|(x,1)∈R}={x|x-1 is an integer}={x|x-1=k for some k∈Z}
={x|x=k+1 for some k∈Z}={k+1|k∈Z}={...,-2+1,-1+1,0+1,1+1,2+1,...}=Z
For the other class, we have
[1/2]={x|(x,1/2)∈R}={x|x-1/2 is an integer}={x|x-1/2=r for some r∈Z}
={x|x=r+1/2 for some r∈Z}={r+1/2|r∈Z}={...,-2+1/2,-1+1/2,0+1/2,1+1/2,..}
={...,-3/2,-1/2,1/2,3/2,...}={r/2| r is an odd integer}
