Is $xRy$ iff $x$ and $y$ were born less than one week apart reflexive?

Question

So I asked this question before without getting a solid answer. I went and studied a bit more about binary relations and reflexive relations. I understand the theory, but am unsure about whether my application of the the theory is correct in my answers.

For the Question below:

Let $A$ be the set of all people who have ever lived. For $x$,$y$∈$A$, $xRy$ if and only if $x$ and $y$ were born less than one week apart. Determine:

(i) Whether or not the relation $R$ is reflexive;

I have stated that, $xRy$ is NOT reflexive, as for the relation $xRy$, ∀ $x∈A$ is not equal ∀ $y∈A$

is this right? if not could someone tell me why not and possibly show me how to get the right answer for this particular question.

Answer 1

It is reflexive!

$xRx$ is: are you born less than one week apart... from yourself? But of course.