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 $R = \{(x, y): x \text{ is the father of } y\}$.

(NONE) $R = \{(x, y): x \text{ is the father of } y\}$
$(x, x) \notin R$ because a person cannot be their own father.
Therefore,$R$ is not reflexive.
Now,let $(x, y) \in R$.
This implies $x$ is the father of $y$.
Then $y$ cannot be the father of $x$ (as $y$ is the child of $x$).
Therefore,$(y, x) \notin R$.
Thus,$R$ is not symmetric.
Now,let $(x, y) \in R$ and $(y, z) \in R$.
This implies $x$ is the father of $y$ and $y$ is the father of $z$.
Then $x$ is the grandfather of $z$,not the father of $z$.
Therefore,$(x, z) \notin R$.
Thus,$R$ is not transitive.
Hence,$R$ is neither reflexive,nor symmetric,nor transitive.