Question

A relation $R$ on a set $A$ is a partial order if it is

• A. Reflexive, antisymmetric and transitive
• B. Reflexive, asymmetric and transitive
• C. Reflexive, symmetric and transitive
• D. Repetitive, symmetric and transformative

Hint:

Partial orders must be reflexive, antisymmetric, and transitive—not symmetric or asymmetric.

Answer 1

The Correct Option is A

A relation \(R\) is a partial order on a set if:
- It is reflexive: \(aRa\)
- It is antisymmetric: if \(aRb\) and \(bRa\) then \(a = b\)
- It is transitive: \(aRb\) and \(bRc\) implies \(aRc\)
This defines a partially ordered set (poset).