The less-than relation, <, on reals is A. a partial ordering since it is asymmetric and reflexive B. a partial ordering since it is antisymmetric and reflexive C. not a partial ordering because it is not asymmetric and not reflexive D. not a partial ordering because it is not antisymmetric and reflexive E. none of the above

GATE 1993 · Discrete Mathematics · Partial Order · easy

Answer: E. none of the above

1. Test reflexivity of <: Reflexivity requires a < a for all real a. But a < a is always FALSE. So < is NOT reflexive and therefore NOT a partial order. Options A and B both claim < is reflexive - both wrong.
2. Evaluate options C and D: Option C: says < is not asymmetric. But < IS asymmetric (a < b implies b < a is false). So C is wrong. Option D: says < is not antisymmetric and is reflexive. < is irreflexive (not reflexive), so D is also wrong. None of A-D is correct, so E is the answer.