$S$ is this set of all graduates from a university. $xRy$ means that student $x$ first attended the university at the same year student $y$ did.
The answer key says $R$ is reflexive but isn't it possible that only one student entered the university in a year? Does this matter for being reflexive ?
On
No, it doesn’t matter. No matter which student $x$ may be, $x$ first attended the university in the same year that $x$ first attended the university, so $x\mathrel{R}x$.
On
No one can attend the university for the first year at a certain year, while attending the same university for the first time at another time.
Reflexivity asks whether or not all the elements in the domain satisfy the relation with themselves. We don't limit the years in which students began their studies.
That's okay. Reflexive only says that every element of the set is related to itself. If one student $x$ entered the university that year, they still entered it the same year they themselves did, so $xRx$ is still true.