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

Show that set of all parallel lines in any plane is an equivalence relation.

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

The inverse of an equivalence relation is an equvalence 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 defined on the set A of all triangles in a plane as R={(T_(1),T_(2)):T_(1) is similar to T_(2) ) is an equivalence relation.Consider three right angle triangle T_(1) with sides 3,4,5;T_(2),10. sides 5,12,13 and T_(3) with sides 6,8,10. Which triangles among T_(1),T_(2) and T_(3) are related?

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