Question

Let $R$ be a relation on the set $N$ defined by $\left\{\right(x,y)ϵN,2x+y=41\}$. Then $R$ is

• A. reflexive
• B. symmetric
• C. transitive
• D. none of these

Answer 1

The correct option is D none of these

$R=\{(x,y),x,y\in N,2x+y=41\}$

$R$ is not reflexive as $(2,2)\in R$ as $2\cdot 2+2\ne 41$

Also $R$ is not symmetric as $(1,39)\in R$ but $(39,1)\notin R$

Further $R$ is not transitive as $(11,19)\in R,(19,3)\in R$; but $(11,3)\notin R$

Hence, $R$ is neither reflexive nor symmetric and nor transitive.