# Determine the Domain and Range of the Relations: (Ii) S = { ( a , B ) : B = | a − 1 | , a ∈ Z and | a | ≤ 3 } - Mathematics

Determine the domain and range of the relations:

(ii) $S = \left\{ \left( a, b \right) : b = \left| a - 1 \right|, a \in Z \text{ and} \left| a \right| \leq 3 \right\}$

#### Solution

(ii) $S = \left\{ \left( a, b \right) : b = \left| a - 1 \right|, a \in Z \text{ and } \left| a \right| \leq 3 \right\}$

Now,
= -3 -2 ,-1,0,1,2,3

$b = \left| - 3 - 1 \right| = 4$
$b = \left| - 2 - 1 \right| = 3$
$b = \left| - 1 - 1 \right| = 2$
$b = \left| 0 - 1 \right| = 1$
$b = \left| 1 - 1 \right| = 0$
$b = \left| 2 - 1 \right| = 1$
$b = \left| 3 - 1 \right| = 2$

Thus, we have:
b = 4, 3, 2, 1, 0, 1, 2
Or,
S = {(-3,4)(-2,3) ,(-1,2) ,(0,1),(1,0),(2,1),(3,2)}

Domain (S) = {-3,-2,-1,0,1,2,3}

Range (S) = {0, 1, 2, 3, 4}

Concept: Relation
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 2 Relations
Exercise 2.3 | Q 10.2 | Page 21