Question

Determine the domain and range of the following relations :

(i) $R=\left\{\right(a,b):aϵN,a<5,b=4\}$

(ii) S = \{(a, b) : b = |a - 1|, a \epsilon z\) and $|a|\le 3\}$

Answer 1

(i) We have,

R = {$(a,b):aϵN,a<5,b=4$}

$\Rightarrow a=1,2,3,4$ and b = 4

Thus, R = {(1, 4), (2, 4), (3, 4), (4, 4)}

Clearly, Domain (R) = {1, 2, 3, 4} and Range (R) = {4}

(ii) We have,

S = {$(a,b):b=|a-1|,aϵz$ and $|a|\le 3$}

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

For a = - 3, -2, -1, 0, 1, 2, 3 we get

b = 4, 3, 2, 1, 0, 1, 2 respectively

Thus, s = {(-3, 4), (-2, 3), (-1, 2), (0, 1), (2, 1), (3, 2)}

Domain (S) = {(-3, -2, -1, 0, 1, 2, 3)} and Range (R) = {0, 1, 2, 3, 4}