How is this example NOT transitive?

Question

R = {(a,a),(a,b),(b,a),(b,b),(b,c),(c,b),(c,c)}

Relations are seriously driving me insane. I am revising for my exams and I'm so confused on this stuff. I felt like I was getting a grip of it, then I saw this example... please help me.

Answer 1

The relation is not transitive since $a$ is related to $b$, $b$ is related to $c$ but $a$ is not related to $c$.

Answer 2

For transitivity you have to check if $x\sim y$ and $y\sim z$ then $x\sim z$.

The relation is given by your set $R$.

And it is $a\sim b$ and $b\sim c$. Is $a\sim c$?