Show that the relation "is parallel to" on the set S of all straight lines in a plane is an equivalence relation.

What is an equivalence relation? Show that the relation of'similarity' on the set S of all triangle in a plane is an equivalence relation.

Show that the relation ‘is congruent to’ on the set of all triangles in a plane is an equivalence relation

Which one of the following relations on R is an equivalence relation?

Show that the relation R on the set Z of integers, given by R={(a ,\ b):2 divides a-b} , is an equivalence relation.

Show that the relation R on the set Z of integers, given by R={(a ,\ b):2 divides a-b} , is an equivalence relation.

Prove that the relation congruence modulo m on the set Z of all integers is an equivalence relation.

The relation ''is a factor of'' on the set N of all natural number is not

Show that the relation R on the set A{xZ ;0lt=12}, given by R={(a , b): a=b}, is an equivalence relation. Find the set of all elements related to 1.

Show that the relation R on the set A={x in Z ;0lt=xlt=12} , given by R={(a ,\ b): a=b} , is an equivalence relation. Find the set of all elements related to 1.

Show that the relation "geq" on the set R of all real numbers is reflexive and transitive but not symmetric.