Show that each of the relation R in the set `A = {x in Z : 0 le x le 12}`, given by: `R = {(a, b) : a = b}`, is an equivalence relation. Find the set of all elements related to 1 in each case.

Show that each of the relation R in the set A = {x in z : 0 le x le 12} , given by R = {(a,b) : |a-b| is a multiple of 4} is an equivalec relation. Find the set of all elements related to 1 in each case.

Show that the relation R in the set : R = {x : x in Z, 0 le x le 1 2}, given by : R = {(a, b): a = b} are equivalence relations.

Show that the relation R in the set : R = {x : x in Z, 0 le x le 1 2}, given by : R = {(a, b) : |a - b| is a multiple of 4} is an equivalence relation.

Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a – b} is an equivalence relation.

Show that the relation in the set A = { 1 , 2, 3, 4, 5} , given by : R = {(a, b): I a- b I is even} is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of { 2, 4} are related to each other. But no element of { 1, 3, 5} is related to any element of {2, 4}.

Prove that the relation R defined in the set A= { x: x in Z, 0 le x le 12} as R = {(a, b) : abs(a-b) . is divisible by 5} is an equivalence relation.

Prove that the relation R defined in the set A= { x: x in Z, 0 le x le 12} as R = {(a, b) : abs(a-b) . is divisible by 3} is an equivalence relation.

Let A={x in Z:0 le x le 12} . Show that R={(a,b):a,b in A,|a-b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class [2]

Show that the relation R in, the set A = {1, 2, 3, 4, 5} given by R={(a,b):|a-b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5}. is related to any element of. {2, 4).

Prove that the relation R defined on the set Z of integers as R= {(a, b) : 4 divides abs(a-b)} is an equivalence relation.