Question

Determine the domain and range of the relation R defined by

(i) $R=\left\{\right(x,x+5):xϵ(0,1,2,3,4,5\left)\right\}$

(ii) $R=\left\{\right(x,x^3):x$ is a prime number less than 10}.

Answer 1

(i) We have,

R = {(x, x + 5) : x \epsilon (0, 1, 2, 3, 4, 5)}

For the elements of the given sets, we find that

R = {(0, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}

Clearly, Domain (R) = {0, 1, 2, 3, 4, 5} and Rane (R) = {5, 6, 7, 8, 9, 10}

(ii) We have,

$R=\left\{\right(x,x^3):x$ is a prime number less than 10}

For the elements of the given sets, we find that

x = 2, 3, 5, 7

$\therefore (2,8)ϵR,(3,27)ϵR,(5,125),ϵR$ and $(7,343)ϵR$

$\Rightarrow R=\left\{\right(2,8),(3,27),(5,125),(7,343)$

Cleary, Domain (R) = {2, 3, 5, 7} and Range (R) = {8, 27, 125, 343}