Show that the relation R in the set Z of intergers given by
`R ={(a,b):2 ` divides a-b }
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 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 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 each case.

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

The relation R difined the set Z as R = {(x,y) : x - yin Z} show that R is an equivalence relation.

Show that the relation R defined by (a,b) R (c,d) implies a + d = b +c on the set N xxN is an equivalence relation.

Show that the relation R in the set A of points in a plane give by R = {(P,Q) : distance of the point P from the origin is same as the distance of the point Q from the origin} , is an equivalence relation. Further , show that the set equivalence relation . Further , show that the set of all points related to a point P ne (0,0) is the circle passing through P with origin as centre.

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 multiple of 4} is in equivelance.

A = {(1,2,3,......10} The relation R defined in the set A as R = {(x,y) : y = 2x} . Show that R is not an equivalence relation.

The relation R defined on the set of natural numbers as {(a,b) : a differs from b by 3} is given by

Let f: X rarrY be a function. Define a relation R in X given by R = {(a, b): f(a) = f(b)} . Examine whether R is an equivalence relation or not.