Define a relation $R$ on the set $N$ of natural numbers by $R=\{(x, y): y=x+5, x$ is a natural number less than $4 ; x, y \in N\}$. Depict this relationship using roster form. Write down the domain and the range.
$\mathrm{R}=\{(x, y): y=x+5, x$ is a natural number less than $4, x, y \in \mathbf{N}\}$
The natural numbers less than 4 are 1, 2, and 3.
$\therefore R=\{(1,6),(2,7),(3,8)\}$
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 $R=\{6,7,8\}$
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