Let, $A=\left\{1, 2, 3, 4, 5, 6\right\}$

The relation $R$ is defined on set $A$ is

$R=\left\{\left(a, b\right) : b=a+1\right\}$. Therefore, $R=\left\{(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)\right\}$

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