Define an equivalence relation.

Let O be the origin.We define a relation between two points P and Q in a plane if OP=OQ. Show that the relation,so defined is an equivalence relation.

Let O be the origin.We define a relation between two points P and Q in a plane if OP=OQ. Show that the relation,so defined is an equivalence relation.

Let O be the origin. We define a relation between two points P and Q in a plane if O P=O Qdot Show that the relation, so defined is an equivalence relation.

Let O be the origin. We define a relation between two points P and Q in a plane if O P=O Qdot Show that the relation, so defined is an equivalence relation.

Let O be the origin. We define a relation between two points P and Q in a plane if O P=O Q . Show that the relation, so defined is an equivalence relation.

Prove that the relation R in the set of integers Z defined by R = {(x,y) : x - y. is an integer) is an equivalence relation.

Show that the relation R in the set of all natural number, N defined by is an R = {(a , b) : |a - b| "is even"} in an equivalence relation.

Which of the following defined on Z is not an equivalence relation ?

R_1 and R_2 are two equivalence relation defined on set A(ne phi) . Show that R_1capR_2 is an equivalence relation.