Let $R$ be a relation on a set $A$. Is $R$ a partial order?
$A = \{0,1,2,3\}$
$R = \{(0,0), (1,1), (2,0), (2,2), (2,3), (3,2), (3,3)\}$
I know that it's reflexive, not anti-symmetric, and not transitive. I have the answer.
Can someone explain to me why it is not transitive?
It's not transitive because $3$ relates to $2$, $2$ relates to $0$, but $3$ does not relate to $0$.