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 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}.

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

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

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

Show that the relation R in the set A of points in a plane given 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 of all points related to a point P ne (0,0) is the circle passing through P with origin as centre.

Show that the relation R, on the set A={x in ZZ : 0 le x le 12} given by R = {(a,b) : |a-b| is a multiple of 4 and a,b in A } is an equivalance relation on A.

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

Define an equivalence relation. Show that the relation similarity on the set of all triangles in a plene is an equivalence relation.

Prove that the relation R on the set A={a in ZZ:1 |x-y| is a multiple of 4} is an equivalence relation. Find also the elements of set A which are related to 2.