Show that the relation R in the set of all integers, Z defined by `R = {(a, b) : 2 "divides" a - b}` is an equivalence relation.

Prove that the relation R in the set of integers z defined by R = { ( x , y) : x-y is an integer } is an equivalence relation.

Prove that the relation R in the set of integers Z defined by R = {(x,y) : x - y. is an integer) is an equivalence relation.

Show that the relation R in the set of integers given by R= {(a,b) : 5 divides (a - b)} is symmetric and transitive.

Show that the relation R in the set of all natural number, N defined by is an R = {(a , b) : |a - b| "is even"} in an equivalence relation.

Solve that the relation R in the set z of intergers given by R={(x,y):2 divides (x-y)} is an equivalence relation.

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}.

Show that 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 equivalence relation.

Show that the relation R in the set A={x in Z :0lexle12} is given by R={(a,b) : |a-b|" is a multiple of 4"} is an equivalence relation .

Let R be the equivalence relation on z defined by R = {(a,b):2 "divides" a - b} . Write the equivalence class [0].