Show that the relation R is in the set `A={1,2,3,4,5}` given by R={(a, b): |a-b| is divisible by 2}, is an equivalence relation. Write all the equivalence classes of R.

Show that the relation R on the set A={1, 2, 3, 4, 5} given by R={(a,b): abs(a-b) is even} in an equivalence ralation.

Prove that the relation R on the set Z of all integers defined by R={(a, b):a-b is divisible by n} is an equivalence relation.

Show that the relation S in set A={x in Z : 0 le x le 12} given by S={(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.

Show that the relation R on the set A = {1,2,3,4,5) given by R = {(a,b): la -bl is even)} is an equivalence relation. Also, show that all 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).

Write the equivalence class [3]_7 as a set.

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

Let R is the equivalence in the set A = {0, 1, 2, 3, 4, 5} given by R = {(a, b) : 2 divides (a - b)}. Write the equivalence class [0].

If the relation R is defined on the set A={1,2,3,4,5} by R={a,b} : |a^(2)-b^(2)| lt 8 . Then, find the relation R.

Check whether the relation R defined on the set A = {1,2,3,4,5,6} as R = {(x,y):y is divisible by x} is reflexive, symmetric and transitive.