Determine whether the following relation is reflexive,symmetric,and transitive:
Relation $R$ in the set $A$ of human beings in a town at a particular time given by $R = \{(x, y): x \text{ and } y \text{ work at the same place}\}$.

(N/A) $R = \{(x, y): x \text{ and } y \text{ work at the same place}\}$
$1. \text{Reflexivity:}$
For any person $x \in A$,$x$ works at the same place as $x$. Therefore,$(x, x) \in R$ for all $x \in A$. Thus,$R$ is reflexive.
$2. \text{Symmetry:}$
Let $(x, y) \in R$. This means $x$ and $y$ work at the same place. Consequently,$y$ and $x$ also work at the same place. Therefore,$(y, x) \in R$. Thus,$R$ is symmetric.
$3. \text{Transitivity:}$
Let $(x, y) \in R$ and $(y, z) \in R$. This means $x$ and $y$ work at the same place,and $y$ and $z$ work at the same place. It follows that $x$ and $z$ work at the same place. Therefore,$(x, z) \in R$. Thus,$R$ is transitive.
Conclusion: The relation $R$ is reflexive,symmetric,and transitive.