Determine the domain and range of the following relations:

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

Now,

$a=-3,-2,-1,0,1,2,3$

$b=|-3-1|=4$

$b=|-2-1|=3$

$b=|-1-1|=2$

$b=|0-1|=1$

$b=|1-1|=0$

$b=|2-1|=1$

$b=|3-1|=2$

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