Question

Let $R$ be a relation defined on $N$ as $R=\left\{\right(x,y)|x,y\in N,2x+y=41\}.$ Then $R$ is

• A. a symmetric relation
• B. both symmetric and transitive relation
• C. Neither reflexive nor symmetric nor transitive relation
• D. Symmetric relation but not transitive relation

Answer 1

The correct option is C Neither reflexive nor symmetric nor transitive relation

$R=\left\{\right(1,39),(2,37),(3,35),(4,33),(5,31),(6,29),(7,27),(8,25),(9,23),(10,21),(11,19),(12,17),(13,15),(14,13),(15,11),(16,9),(17,7),(18,5),(19,3),(20,1\left)\right\}$

$R$ is not reflexive relation as$(1,1)\notin R$
$R$ is not symmetric relation as$(1,39)\in R$ but $(39,1)\notin R$
$R$ is not transitive relation as $(15,11)\text{and}(11,19)\in R$ but $(15,19)\notin R$
$\therefore R$ is neither reflexive nor symmetric nor transitive relation