Understanding Transitivity in Relations: Why R on A={0,1,2,3} is Not Transitive

[physicsuser]

let R be a relation on the set A={0,1,2,3}. If R={(0,0),(0,2),(2,0),(2,2),(2,3),(3,2),(3,3)} why it is not transitive?

VaVbVc (a,b) in R and (b,c) in R implies (a,c) in R a,b,c in A. (V is the 'for all' symbol)

so there are

(0,2) and (2,0) with (0,0)
(2,0) and (0,2) with (2,2)
(2,3) and (3,2) with (2,2)
(3,2) and (2,3) with (3,3)

How is it not transitive?

 

[shmoe]

You haven't considered all the possibilites. For (0,2) write down all pairs of the form (2,c). You only considered one such pair, there are more. For each of these, check if (0,c) is in your set.

 

[physicsuser]

You haven't considered all the possibilites. For (0,2) write down all pairs of the form (2,c). You only considered one such pair, there are more. For each of these, check if (0,c) is in your set.

Thank you! Me so blind lol. (0,2) and (2,3) but NO (0,3). Ahhhh it makes me mad.