Let R be relation defined on the set of natural number N as follows: \[\mathbf{R}\text{ }=\text{ }\{\left( \mathbf{x},\text{ }\mathbf{y} \right):\text{ }\mathbf{x}\in \mathbf{N},\text{ }\mathbf{y}\in \mathbf{N},\text{ }\mathbf{2x}\text{ }+\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{41}\}\]. Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive.

Home » Let R be relation defined on the set of natural number N as follows: . Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive.

Let R be relation defined on the set of natural number N as follows:

$\mathbf{R}\text{ }=\text{ }\{\left( \mathbf{x},\text{ }\mathbf{y} \right):\text{ }\mathbf{x}\in \mathbf{N},\text{ }\mathbf{y}\in \mathbf{N},\text{ }\mathbf{2x}\text{ }+\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{41}\}$

. Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive.

Let R be relation defined on the set of natural number N as follows:

$\mathbf{R}\text{ }=\text{ }\{\left( \mathbf{x},\text{ }\mathbf{y} \right):\text{ }\mathbf{x}\in \mathbf{N},\text{ }\mathbf{y}\in \mathbf{N},\text{ }\mathbf{2x}\text{ }+\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{41}\}$

. Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive.

Given function:

$\mathbf{R}\text{ }=\text{ }\{\left( \mathbf{x},\text{ }\mathbf{y} \right):\text{ }\mathbf{x}\in \mathbf{N},\text{ }\mathbf{y}\in \mathbf{N},\text{ }\mathbf{2x}\text{ }+\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{41}\}$

.

So, the domain =

$\left\{ 1,\text{ }2,\text{ }3,\text{ }\ldots ..,\text{ }20 \right\}\text{ }[Since,\text{ }y\in N\text{ }]$

Finding the range, we have

$R\text{ }=\text{ }\left\{ \left( 1,\text{ }39 \right),\text{ }\left( 2,\text{ }37 \right),\text{ }\left( 3,\text{ }35 \right),\text{ }\ldots .,\text{ }\left( 19,\text{ }3 \right),\text{ }\left( 20,\text{ }1 \right) \right\}$