LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

RELATION & MAPPING - DOMAIN & RANGE

__Domain & Range –__

**The set of all the first elements (or
components) of the ordered pairs of a relation is considered to be the domain of the relation. The set of all the second elements (or components) of
the ordered pairs of a relation is to be considered the range of the relation. In
the preceding two examples the domains are {2, 3, 5} and {7, 9, 11}, while the
ranges are {8, 27, 125} and {14, 22, 27} respectively. Notice that in the first
case, domain = set A and range = set B, but in the second case, domain ≠ set A
and range ≠ set B. In fact, domain ⊂ set A and range ⊂ set B.**

**Example.) Let A = {0, 1, 2, 3, 4, 5}, B = {1,
2, 3, 5, 7, 9} and R = {{(a, b) : a Є A,
b Є B and a + b = 8}**

**1)
Find R and represent it by an arrow diagram,**

**2)
Find the domain and range of R**

**Ans.)**

**As per the
given condition, R = {(a, b) : a Є A, b
Є B and a + b = 10},**

**Clearly, 1 +
9 = 10, 5 + 5 = 10, 3 + 7 = 10**

**So, (1, 9) Є
R, (5, 5) Є 10, and (3, 7) Є 10**

**1) R = {(1, 9), (5, 5), and (3, 7)}**

**The arrow
diagram for R is shown alongside …………………………………………(1) (Ans.)**

**2) The domain of R = {1, 3, 5}, and the range of
R = {5, 7, 9}….…………(2) (Ans.)**