In the following cases, for the given relation R on the set S, determine which are equivalence relations:
S is the set of all people in the world today, a R b `iff` a and b have same father.

In the following cases, for the given relation R on the set S, determine which are equivalence relations: S is the set of all people in the world today, a R b iff a lives within 100 kilometres f b.

For the given relation R on a set S, determine which are equivalence relations : (i) S is the set of all rational numbers a R b iff a= b. (ii) S is the set of all real numbers iff : (I) |a |= |b| (II) a ge b .

If relation R defined on set A is an equivalence relation, then R is

In order that a relation R defined on a non-empty set A is an equivalence relation, it is sufficient, if R

The smallest equivalence relation R on set A ={1,2,8} is=

Consider the set A=(a,b,c). Give an example of a relation R on A which is an equivalent 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.

Let R be the relation on the set R of all real numbers defined by a R b Iff |a-b| le1. Then R is

If R_1 and R_2 are equivalence relations in a set A, show that R_1 nn R_2 is also an equivalence relation