Given the set $A$ of all human beings in a town at a particular time and $R=\{(x,y):x \text{and y live in the same locality}\}$

If $x$ lives in a locality, $\rightarrow$ obviously $(x,x) \in R$. Hence $R$ is reflexive.

If $x$ and $y$ live in a locality, i.e., if $(x,y) \in R$ $\rightarrow$ it follows that $y\; $and $x$ live in the same locality, i.e, $(y,x) \in R$. Hence $R$ is symmetric.

If $x$ and $y$ live in a locality, i.e., if $(x,y) \in R$ and if $y$ and $z$ live in the same locality, i.e., if $(y,z) \in R$ $\rightarrow$ it follows that $x\; $and $z$ also live in the same locality, i.e, $(x,z) \in R$. Hence $R$ is transitive.