Question

Determine the domain and range of the following relations:

(i) R = {(a, b) : a ∈ N, a < 5, b = 4}
(ii) $S=\left\{\left(a,b\right):b=\left|a-1\right|,a\in Z\mathrm{and}\left|a\right|\le 3\right\}$

Answer 1

(i) R = {(a, b) : a ∈ N, a < 5, b = 4}
We have:
a = 1, 2, 3, 4
b = 4
R = {(1, 4), (2, 4), (3, 4), (4, 4)}
Domain (R) = {1, 2, 3, 4}
Range (R) = {4}

(ii) $S=\left\{\left(a,b\right):b=\left|a-1\right|,a\in Z\mathrm{and}\left|a\right|\le 3\right\}$
Now,
a = $-$3, $-$2, $-$1, 0, 1, 2, 3
$$\begin{gathered} b=\left|-3-1\right|=4 \\ b=\left|-2-1\right|=3 \\ b=\left|-1-1\right|=2 \\ b=\left|0-1\right|=1 \\ b=\left|1-1\right|=0 \\ b=\left|2-1\right|=1 \\ b=\left|3-1\right|=2 \end{gathered}$$
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}