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
Answer:A
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
Explanation: 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.