(i)\\\\(A=\\left\\{x\\in Z:0\\leq x\\leq 12\\right\\}=\\left\\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\\right\\}\\\\)\\\\(R=\\left\\{(a, b):|a-b| \ ext{is a multiple of 4}\\right\\}\\\\)For any element \\\\(a\\in A\\\\), we have \\\\((a, a)\\in R\\\\) as \\\\(|a-a|=0\\\\) is a multiple of \\\\(4\\\\).\\\\(\ herefore R\\\\) is reflexive.Now, let \\\\((a, b)\\in R\\Rightarrow |a-b|\\\\) is a multiple of \\\\(4\\\\).\\\\(\\Rightarrow |-(a-b)|=|b-a|\\\\) is a multiple of \\\\(4\\\\).\\\\(\\Rightarrow (b, a)\\in R\\\\)\\\\(\ herefore \\\\) is symmetric.Now, let \\\\((a, b), (b, c)\\in R\\\\)\\\\(\\Rightarrow |a-b|\\\\) is a multiple of \\\\(4\\\\) and \\\\(|b-c|\\\\) is a multiple of \\\\(4\\\\).\\\\(\\Rightarrow (a-b)\\\\) is a multiple of \\\\(4\\\\) and \\\\((b-c)\\\\) is a multiple of \\\\(4\\\\).\\\\(\\Rightarrow (a-c)=(a-b)+(b-c)\\\\) is a multiple of \\\\(4\\\\).\\\\(\\Rightarrow |a-c|\\\\) is a multiple of \\\\(4\\\\).\\\\(\\Rightarrow (a, c)\\in R\\\\).\\\\(\ herefore R\\\\) is transitive.Hence, \\\\(R\\\\) is an equivalence relation.The set of elements related to \\\\(1\\\\) is \\\\(\\left\\{1, 5, 9\\right\\}\\\\) since \\\\(|1-1|=0\\\\) is a multiple of \\\\(4\\\\),\\\\(|5-1|=4\\\\) is a multiple of \\\\(4\\\\), and \\\\(|9-1|=8\\\\) is a multiple of \\\\(4\\\\)Hence, \\\\(R\\\\) is an equivalence relation.(ii)\\\\(A=\\{x\\in Z: 0\\leq x\\leq 12\\}=\\{0,1,2,3,4,......,11,12\\}\\\\)\\\\(R=\\left\\{(a, b):a=b\\right\\}=\\{(0,),(1,1),(2,2),........,(11,11),(12,12)\\}\\\\)For any element \\\\(a\\in A\\\\), we have \\\\((a, a)\\in R\\\\), since \\\\(a=a\\\\).\\\\(\ herefore R\\\\) is reflexive.Now, let \\\\((a, b)\\in R\\\\).\\\\(\\Rightarrow a=b\\\\)\\\\(\\Rightarrow b=a\\\\)\\\\(\\Rightarrow (b, a)\\in R\\\\)\\\\(\ herefore R\\\\) is symmetric.Now, let \\\\((a, b)\\in R\\\\) and \\\\((b, c)\\in R\\\\).\\\\(\\Rightarrow a=b\\\\) and \\\\(b=c\\\\)\\\\(\\Rightarrow a=c\\\\)\\\\(\\Rightarrow (a, c)\\in R\\\\)\\\\(\ herefore R\\\\) is transitive.Hence, \\\\(R\\\\) is an equivalence relation.The elements in \\\\(R\\\\) that are related to \\\\(1\\\\) will be those elements from set \\\\(A\\\\) which are equal to \\\\(1\\\\).Hence, the set of elements related to \\\\(1\\\\) is \\\\(\\left\\{1\\right\\}\\\\).