Transitive relation.

Question

I have read transitive relation, if $a\mathrel R b$ and $b\mathrel Rc$ then $a\mathrel Rc$. But suppose we have a set of first cousins.

$$\mathrel R: \{(a,b),(a,c)\}$$

Where $a$, $b$ and $c$ are first cousins. Can anyone please help if the set $\mathrel R$ transitive?

Answer 1

Not transitive, b and c could be siblings.

Answer 2

Well, the set is not transitive. Transitive means that $aRb\wedge bRc\Rightarrow aRc$.

The point is: If the premise is not satisfied, the whole assertion is true.