The relation R ~is defined in the set \ 1, 2, 3, 4, 5, 6\ as R = \...

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 $(1,2) \in \mathbb{R}$ but $(2,1) \notin R$. Therefore, R is not symmetric.

Now, $(1,2) , (2,3) \in \mathbb{R}$ but $(1,3) \notin R$. Therefore, $R$ is not transitive.

Hence, $R$ is neither reflexive nor symmetric nor transitive