Question

Which of the following relation is a partial order as well as an equivalence relation?

(a) equal to(=)

(b) less than(<)

(c) greater than(>)

(d) not equal to(!=)

I have been asked this question by my school principal while I was bunking the class.

This is a very interesting question from Graphs in chapter Graphs of Discrete Mathematics

Answer 1

Right choice is (a) equal to(=)

The explanation: The identity relation = on any set is a partial order in which every two distinct elements are incomparable and that depicts the relation of both a partial order and an equivalence relation. For non-linear orders, there are many advanced properties of posets.