$R =\{( x , y ): x$ and $y $  live in the same locality $\}$

Clearly, $( x , x ) \in R$ as $x$ and $x$ is the same human being.

$\therefore R$ is reflexive.

If $(x, y) \in R,$ then $x$ and $y$ live in the same locality.

$\Rightarrow y$ and $x$ live in the same locality.

$\Rightarrow(y, x) \in R$

$\therefore R$ is symmetric.

Now, let $(x, y) \in R$ and $(y, z) \in R$

$\Rightarrow x$ and $y$ live in the same locality and $y$ and $z$ live in the same locality.

$\Rightarrow x$ and $z$ live in the same locality.

$\Rightarrow(x, z) \in R$

$\therefore R$ is transitive.

Hence, $R$ is reflexive, symmetric and transitive.