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Equivalence Relation
A relation which is reflexive, symmetric and transitive is called the Equivalence relation.
i.e., A relation R in a set A is called equivalence if it satisfies the following conditions.

Remarks:
- The smallest equivalence relation in set A is the relation of equality in A.
- The largest equivalence relation in A is A x A.
Inverse Relation
Let R Í A x B be a relation from A to B. Then the inverse of R, denoted by R-1 is a relation from B to A, defined as 
Example 1:
If R = {(1,2), (1,5),(2,4),(3,5)}
Domain of R-1= {2, 5, 4} = Range of R
Range of R-1= {1, 2, 3} = Domain of RExample 2:
If f is a relation from a set A to set B such that f Í f-1 then, prove that f = f-1.
Suggested answer:

From (i) and (ii),

Some important relations
- On the set of positive integers Z+, the relation “a divides b” is
- reflexive
- not symmetric
- transitive
- On the set of positive integers Z+, the relation "a
- not reflexive
- not symmetric
- transitive
- On the set of triangles, the relation “similar to” is
- reflexive
- symmetric
- transitive
- On the set of lines in a plane, the relation “parallel to” is
- reflexive
- symmetric
- transitive
- On the set of lines in a plane, the relation “perpendicular to” is
- not reflexive
- symmetric
- not transitive
- On the universal set of sets, the relation “subset of” is
- reflexive
- not symmetric
- transitive
- On the universal set of sets, the relation “subset of” is an
- On the set of integers, the relation “congruence” is an equivalence relation.

