Question

The relation ≤ is a partial order if it is ___________

(a) reflexive, antisymmetric and transitive

(b) reflexive, symmetric

(c) asymmetric, transitive

(d) irreflexive and transitive

I have been asked this question at a job interview.

This question is from Graphs in section Graphs of Discrete Mathematics

Answer 1

The correct answer is (a) reflexive, antisymmetric and transitive

The explanation is: Let A is a set and ≤ is a relation on A, then ≤ is a partial order if it satisfies reflexive, antisymmetric, and transitive, i.e., for all x, y and z in P. That means, x ≤ x (reflexivity);

 if x ≤ y and y ≤ x then x = y (antisymmetry) and if x ≤ y and y ≤ z then x ≤ z (transitivity).