Question

Let R be a relation defined on the set of natural numbers N as
$R=\{(x,y):xϵN,yϵN,2x+y=41\}$ Check if
R is (i) reflexive (ii) symmetric

Answer 1

The Relation $R$ can be written as $R=\{(1,39),(2,37),(3,35),...(10,21),(11,19),...(19,3),(20,1)\}$

$\therefore$ Domain of $R=\{1,2,3,...19,20\}$

Range of $R=\{39,37,35,.....9,7,5,3,1\}$ $R$ is not reflexive.

Since $(x,x)\notin R\forall x\in N$

For exemple $(1,1)\notin R$

$R$ is not symmetric since $(1,39)\in R$ but $(39,1)\notin R.$