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

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.

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.

Show that the relation R in the set {1,2,3} given by R = {(1,2), (2,1) is symmetric but neither reflexive nor transitive.

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

Let f: X to Y 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.

If R is a relation on the set A={1,2,3,4,5,6,7,8,9}"given by "xRyiffy=3x , then R =

Show that the relation R in the set {1,2,3} given by R = {(1,1) ,(2,2),(3,3) , (1,2) ., (2,3)} is reflexive but neither symmetric nor transitive.