Question

If a relation $R$ is defined between $x$ and $y$ such that $R=\left\{\right(x,y):4x+y\ge 34$ where $x,y\in N\}$, then the relation $R$ is

• A. Reflexive but not symmetric
• B. Symmetric but neither reflexive nor transitive
• C. Transitive and symmetric but not reflexive
• D. Neither of reflexive, symmetric or transitive

Answer 1

The correct option is D Neither of reflexive, symmetric or transitive

Reflexive:
Let take an element $(3,24)$
For being reflexive $(x,x)=(3,3)$ should belong to relation $R$: $4\times 3+3=12\ngeqq 34$ So relation R is not reflexive.
For symmetric take element $(8,5)$ for being symmetric $(x,x)=(5,8)$ should belong to relation $R$ $4\times 5+8=28\ngeqq 34$ So relation R is not symmetric.
For transitive take elements $(x_1,x_2)=(4,18)$ and $(x_2,x_3)=(18,2)$for being transitive $(x_1,x_3)=(4,2)$ should belong to relation $R$
$4\times 4+2=18\ngeqq 34$ So relation R is not transitive.
So Relation $R$ is neither reflexive,symmetric. nor transitive.