During studying I stumbled upon a thought regarding reflexive relations. I'm familiar that a relation is reflexive if for each element $x$ in a set $S$, $xRx$. (∀x ∈ S: xRx)? Such as something like this $<1,1>,<2,2>$. However is the following deemed a reflexive relation? $$(<1,2>,<2,3>,<3,4>,<4,1>)$$
I'm unsure, as my gut feeling tells me that this relation is not reflexive, yet I am unsure. The addition of $$(<1,1>,<2,2>,<3,3>,<4,4>)$$ would surely make it reflexive if it already was not? Is it already reflexive?
With "chaining" i refer to that the last tuple refers to the start. So something akin to a relation from 4 to 1