Question

Define a relation $R$ on the set $N$ of natural numbers by $R=\left\{\right(x,y):y=x+5,x$ is a natural number less than $4;x,y\in N\}$. Depict this relationship using roster form. Write down the domain and the range.

Answer 1

Given definition of $R$ is
$R=\left\{\right(x,y):y=x+5,x\text{is a natural number less than 4},x,y\in N\}$
The natural numbers less than $4$ are $1,2$ and $3$
$\therefore R=\left\{\right(1,6),(2,7),(3,8\left)\right\}$
The domain of $R$ is the set of all first elements of the ordered pairs in the relation
$\therefore$ Domain of $R=\{1,2,3\}$
The range of $R$ is the set of all second elements of the ordered pairs in the relation
$\therefore$ Range of $R=\{6,7,8\}$