Question

The less-than relation, <, on a set of real numbers is ______

(a) not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric

(b) a partial ordering since it is asymmetric and reflexive

(c) a partial ordering since it is antisymmetric and reflexive

(d) not a partial ordering because it is not antisymmetric and reflexive

This question was addressed to me at a job interview.

I would like to ask this question from Relations in division Relations of Discrete Mathematics

Answer 1

The correct option is (a) not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric

To explain I would say: Relation less than a set of real numbers is not antisymmetric and reflexive. Relation is not POSET because it is irreflexive. Again, aRb != bRa unless a=b and so it is antisymmetric. A relation may be ‘not asymmetric and not reflexive but still antisymmetric, as {(1,1) (1,2)}. So, the relation is not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric.