1. Reflexive Relation:
R is a relation in A and for every a Î A, (a,a) Î R then R is
said to be a reflexive relation.
Example:
Every real number is equal to itself. Therefor "is equal to " is a reflexive relation in the set of real numbers.
2. Symmetric Relation:
R is a relation in A and (a,b) Î R implies (b,c) Î R then R
is said to be a symmetric relation.
Example:
In the set of all real numbers "is equal to" relation is symmetric.
3. AntiSymmetric Relation:
R is a relation in A. If (a,b) Î R and (b,a) Î R implies a =
b, then R is said to be an antisymmetric relation.
Example:
In set of all natural numbers the relation R defined by "x divides y if and only if (x,y) Î
R" is antisymmetric. For xy and yx then x = y.
4. Transitive Relation:
R is a relation in A if (a,b) Î R and (b,c) Î R implies (a,c)
Î R is called a transitive relation.
Example:
In the set of all real numbers the relation "is equal to" is a transitive relation. For a = b, b = c implies a = c.
5. Equivalence Relation:
A relation R in a set A is said to be an equivalence relation if it is reflexive, symmetric and transitive.
Example:
In the set of all real numbers the relation "is equal to" is an equivalence relation for a Î
R, a = a, b = a implies b = a and a = b, b = c implies a = c.
Directions: Choose the correct answer. Also write at least 10 examples of your own.
