Question

Let $A=\{1,2,3,4\}$ and $R=\left\{\right(2,2\left)\right(3,3\left)\right(4,4\left)\right(1,2\left)\right\}$ be a relation on $A$. Then what is the nature of ${}^{\prime }{R}^{\prime }$?

Answer 1

Reflexive:

Since $(1,1)$ is not in $R$.
So, it is not a reflexive relation on $A$.
Symmetric:

Clearly $(1,2)\in R$ and $(2,1)\notin R$
So, it is not symmetric on $A$.
Transitive:

We find that $(1,2),(2,2)\in R,(1,2)\in R$

Similarly for $(2,2)(3,3)(4,4)$.

So, it is transitive on $A$.