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 ∈ N}. Depict this relationship using roster form. Write down the domain and the range.
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 ∈ N}. Depict this relationship using roster form. Write down the domain and the range.

The connection R is given by:

    \[R\text{ }=\text{ }\{\left( x,\text{ }y \right):\text{ }y\text{ }=\text{ }x\text{ }+\text{ }5,\]

x is a characteristic number under 4, x, y ∈ N}

The regular numbers under 4 are 1, 2, and 3.

Along these lines,

    \[R\text{ }=\text{ }\left\{ \left( 1,\text{ }6 \right),\text{ }\left( 2,\text{ }7 \right),\text{ }\left( 3,\text{ }8 \right) \right\}\]

Presently,

The space of R is the arrangement of all first components of the arranged sets in the connection.

Thus, Domain of

    \[R\text{ }=\text{ }\left\{ 1,\text{ }2,\text{ }3 \right\}\]

The scope of R is the arrangement of the entire second components of the arranged sets in the connection.

Thus, Range of

    \[R\text{ }=\text{ }\left\{ 6,\text{ }7,\text{ }8 \right\}\]