For each relation, determine transitivity?

Question

Why is b) not transitive? I checked (a,b)^(b,a)-->(a,a) which works and the c,c and d,d are related to eachoter so there also transitive, what am i doing wrong?

Answer 1

$b$ is related to $a$ and $a$ is related to $b$ so $b$ should be related to $b$ but it isn't.

Answer 2

You are missing (b,b).

The relation is not transitive because (b,a) and (a,b) should imply (b,b).

Answer 3

There is no $(b,b)$ even though $(a,b), (b,a)$ are present.