Venn diagram: In this method the relation is indicated by using a Venn diagram. For example, 2 is a factor of 2, 6, 12
3
is a factor of 3, 6, 12
6 is a factor of 6, 12
12 is a factor of 12
Domain: It is the set of all elements which are the first component of the set of ordered pairs and represent a particular relation.
For example: If R = { ( 1, 1 ), ( 1, 2), ( 2, 1 ), (2, 2 ) } then the domain is { 1, 2 }
Range: It is a set of all the second components of the ordered pair and represent a relation.
For example : R = { ( a, c ), ( a, d ), ( b, c ), ( b, d ) } then range = {c, d }
Properties of relations
Reflexive property: A relation R is reflexive if x R x is true for all x, belonging to the domain of R.
For example R = { ( 1, 1 ), ( 2, 2 ), ( 3, 3 ), ( a, a ) }
Symmetric relation: A relation R is symmetric, if for every x R y that is true also have y R x (which is also true).
In symbols 1) ( x, y ) Î R Þ ( y, x ) Î R
D ABC ~ D PQR Þ D PQR Þ D ABC
~ = similar to
Transitivity: A relation R is transitive if x R y and y R z implies that x R z.
i.e. x R y and y R z Þ x R z
For example, 8 is greater than 6 and 6 is greater 4, then 8 is greater than 4. i.e.
8 > 6, 6 > 4 Þ 8 > 4.
If a relation is reflexive, symmetric and transitive then it is an Equivalence relation.

Index
6.1 Relations
6.2 Functions 6.3 Variation
Chapter 7
