Prove that the relation " friendship " is not an equivalence relation on the set of all people in Chennai.

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

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.

Prove that the intersection of two equivalence relations in a set is an equivalence relation and give an example to show that the union of two equivalence relations in a set is not necessarily an equivalence relation.

Prove that set of similar triangles, 'is similar to' is an equivalence relation

Show that the relation S in set A={x in Z : 0 le x le 12} given by S={(a, b):a, b in A, |a-b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1.

Show that the relation R in the set Z of integers given by R{(x,y):6" divides "x-y} is an equivalence relation. Find the set of all elements related to 0.

Show that the relation S in the set A={x in Z:0<=x<=12} given by S={(a,b):a,b epsilon Z,^(-)|a-b| is divisible by 4} is an equivalence relation.Find the set of all elements related to 1.