Question

The relation $R$ defined in the set $\{1,2,3,4,5,6\}$ as $R=\left\{\right(a,b):b=a+1\}$ is

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

Answer 1

The correct option is D None of these

Let $A=\{1,2,3,4,5,6\}$
Relation $R$ is defined on set $A$ as

$R=\left\{\right(a,b):b=a+1\}$

$\therefore R=\left\{\right(1,2),(2,3),(3,4),(4,5),(5,6\left)\right\}$
Now, $6\in A$ but $(6,6)\notin R$
Therefore, $R$ is not reflexive.
It can be observed that $(1,2)\in R$ but $(2,1)\notin R$.
Therefore, $R$ is not symmetric.
Now. $(1,2),(2,3)\in R$ but $(1,3)\notin R$.

Therefore, $R$ is not transitive.
Hence, $R$ is neither reflexive nor symmetric nor transitive.