So, as far as binary relations go, I have a firm grasp on the symmetric, anti-symmetric, and reflexive relations. However, when it comes to transitive relations, I run into a block.
In this problem, for example, I had to determine the transitive closures for the given set that contained: (1,1) (1,2) (2,3) (3,2) (4,4)
The additional elements that would enable this set to be a transitive relation were: (1,3) (2,2) (3,3)
I think I understand that if there is a (1,2) and a (2,3) then there must also be a (1,3). I see that there is a (2,3), but why doesn't there have to be a (3, 4) and a (2,4)? I need some enlightenment as to how I can properly go about determining transitive closures, or determining if a completed relation set includes the right elements to make it transitive.