Question

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

• A. Reflexive
• B. Symmetric
• C. Transitive
• D. None of these

Answer 1

The correct option is D None of these

On the set N of natural numbers,
$R=\left\{\right(x,y);x,yϵN,2x+y=41\}.$
Since $(1,1)\text{/}ϵR$ as $2.1+1=3\ne 41$. So, R is not reflexive. Where R is the Relation.
$(1,39)ϵRbut(39,1)\text{/}ϵR$. So R is not symmetric (20, 1)
$(1,39)ϵR$. But $(20,39)\text{/}ϵR$, So R is not transitive.