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

Question

$\begin{array}{1 1} \text{Domain of R={1,2,3.....20} Range of R ={1,3,.......,37,39} R is not transitive, not symmetric, not reflexive} \\ \text{Domain of R={1,2,3.....20} Range of R ={1,3,.......,37,39} R is transitive, not symmetric, not reflexive} \\ \text{Range of R={1,2,3.....20} Domain of R ={1,3,.......,37,39} R is not transitive, not symmetric, not reflexive} \\ \text{Range of R={1,2,3.....20} Domain of R ={1,3,.......,37,39} R is transitive, not symmetric, not reflexive} \end{array}$