How come 2) is transitive and not 1)

1) R_1 = (1,1) (1,2) (2,1)

2) R_2 = (2,1) (3,1) (3,2) (4,1) (4,2) (4,3)

Definition of transitive relation states that for every(a,b,c) belongs to R

(a,b)belongs to R AND (b,a)belongs to R then (a,c) belongs to R.

So how come 1) is NOT transitive and 2) IS transitive?

Can anyone clarify my doubt!?

Thank you.