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

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 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).

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.

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 in the set of real numbers, defined as R = {(a,b): a le b^(2) } is neither reflexive nor symmetric nor transitive.

Show that the relation R on the set A of real numbers defined as R = {(a,b): a lt=b ).is reflexive. and transitive but not symmetric.

Show that the relation R on Z – {0} defined by R={(m,n)|frac[m][n] is power of 5} is an equivalence relation.

Show that the relation R defined on the set Z of all integers defined as R={(x,y):x-y is an integer} is reflexive, symmertric and transtive.