Hi, i've been mulling over this question for a few days now and i've got an answer, but it seems too simple to be correct.

8 = for all

R is relation

R is useful iff:

(u1) (8x¬(xRx)

(u2) 8xyz((xRy ^ yRz) implies (xRz))

(u3) 8xyz(xRy implies (xRz OR zRy))

Consider the relation ‘greater than’ on Natural numbers. Is it useful? Good? Cool?

I just need a true or false for each, but they all seem to be true (there are several more examples other than these three). I think i'm going about it the wrong way, and any advice to kick me off would be much apprieciated.