Question

How do you find the domain and range?

Answer 1

Hint: Set of all first components of the ordered pairs belonging to R is the domain of R and set of all second components of the ordered pairs belonging to R are known as the range of R.

Complete step-by-step answer:
DOMAIN: Let R be a relation from a set A to a set B. Then the set of all first components or coordinates of the ordered pairs belonging to R is called the domain of R.
Thus, domain of $ R = \left\{ {a:(a,b) \in R} \right\} $
Clearly, the domain of $ R \subseteq A $ .
If $ A = \left\{ {1,3,5,7} \right\},B = \left\{ {2,4,6,8,10} \right\} $ and $ R = \left\{ {\left( {1,8} \right),\left( {3,6} \right),\left( {5,2} \right),\left( {1,4} \right)} \right\} $ is a relation from A to B,
Then,
Domain $ (R) = \left\{ {1,3,5} \right\} $
RANGE: Let R be a relation from a set A to a set B . Then the set of all second components or coordinates of the ordered pairs belonging to R is called the range of R.
Thus, Range of $ R = \left\{ {b:\left( {a,b} \right) \in R} \right\} $
Clearly, range of $ R \subseteq B $
If $ A = \left\{ {1,3,5,7} \right\},B = \left\{ {2,4,6,8,10} \right\} $ and $ R = \left\{ {\left( {1,8} \right),\left( {3,6} \right),\left( {5,2} \right),\left( {1,4} \right)} \right\} $ is a relation from A to B,
Then,
Range $ (R) = \left\{ {8,6,2,4} \right\} $

Note: 1. Relation: Let A and B are two sets .Then a relation R from set A to set B is a subset of $ A \times B $
Thus, R is a relation form A to B $ \Leftrightarrow R \subseteq A \times B $
If R is a relation form a non-void set A to a non-void set B and if $ (a,b) \in R $ ,then we write
 $ a\,R\,b $ which is read as “a is related to b by the relation R “. If $ (a,b) \notin R $ , then we write $ a\,\cancel{R}\,b $ and we say that a is not related to b by the relation R.