Hello, patches!

Here's some help . . .

Which properties do each of the following relations satisfy among the properties:

relexive, symmetric transitive, irreflexive, and antisymmetric?

over the real numbers

. . . True: reflexive

. . . True: symmetric

. . . True: transitive

over the positive integers

. . . True: reflexive

. . . False: not symmetric

. . . True: antisymmetric

. . . True: transitive