Can a relation be non reflexive, non symmetric, non antisymmetric and not transitive?

Question

Lets say I have {a,b,c,d}

I though of (a,b)(b,c) - but this is antisymmetric, right?

Then I though of (a,b)(b,a)(b,c) but this time is transitive

Finally I tried with (a,b)(b,c)(c,d) but again, is this antisymmetric?

Answer 1

$R=\{(a,b), (b,c), (b,a)\}$ will do.

It is obviously non reflexive, also non symmetric because $(c,b)\notin R$; not antisymmetric because $(a,b),(b,a)\in R$ but $a\neq b$, and not transitive beacause $(a,b),(b,c)\in R$ but $(a,c)\notin R$.