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 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 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.

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.

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 R in the set A of all the books in a library of a college, given by R = {(x, y) : x and y have same number of pages} is an equivalence relation.

Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y): x andy have same number of pages} is an equivalence, relation.

Show that relation R defined by R = {(a, b) : a - b is divisible by 3, a, binZ } is an equivalence relation.

Write the following as intervals : {x : x in R, 0 le x < 7}