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

If R is a relation from a set A to t B and S is a relation form B to a set C then the relation S o R

if P,Q are two points on the line 3x+4y+15=0 such that OP=OQ=9 then the area of triangle OPQ is

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

Let A ={1,2,3} be a given set. Define a relation on A which is an equivalence relation on A

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

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; S={(m/n , p/q)"m , n , pandqa r ei n t e g e r ss u c ht h a tn ,q"!="0andq m = p n"} . Then (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation

What is the relation between Cl^(-) and S^(2-) ?

Let R and S be two non - void relations on a set A.

Let Z be the set of all integers and R be the relation on Z defined as R={(a , b); a ,\ b\ in Z , and (a-b) is divisible by 5.} . Prove that R is an equivalence relation.

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.