The relation xRy is defined as "x has drawn a picture of y". R is on the set of all people.
Is this relation: reflexive, irreflexive, symmetric, asymmetric, antisymmetric, transitive ?
What confuses me about this problem is that there is uncertainty involved. If xRy had been defined as "x scored higher on a test than y", then we could definitively say that y did not score higher than x, x did not score higher than himself, etc. However in this case, R doesn't definitively conclude that y did or did not draw a picture of x, or if x also drew a picture of himself, etc.
The Attempt at a Solution
reflexive - no; can't conclude that x drew x
irreflexive - no; can't conclude that it's never the case that x drew x
symmetric - no; can't conclude that y also drew x
asymmetric - yes; in some case both xRy and yRx could be true
antisymmetric - no; if x drew y then we can't always say that y did not draw x
transitive - no; we don't know if yRw means x drew w