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  1. 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

  1. 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 ) }

  2. 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

  3. 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

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