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

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(N/A) The relation is defined as $R = \{(x, y) : y = x + 5, x \in \{1, 2, 3\}, x, y \in N\}$.
Since $x$ is a natural number less than $4$,the possible values for $x$ are $1, 2,$ and $3$.
For $x = 1, y = 1 + 5 = 6$.
For $x = 2, y = 2 + 5 = 7$.
For $x = 3, y = 3 + 5 = 8$.
Thus,in roster form,$R = \{(1, 6), (2, 7), (3, 8)\}$.
The domain is the set of all first elements of the ordered pairs: $\text{Domain} = \{1, 2, 3\}$.
The range is the set of all second elements of the ordered pairs: $\text{Range} = \{6, 7, 8\}$.

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