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Question
Determine the domain and range of the relations:
(ii) \[S = \left\{ \left( a, b \right) : b = \left| a - 1 \right|, a \in Z \text{ and} \left| a \right| \leq 3 \right\}\]
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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,
a = -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}
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