2.7 Partial Orders and Equivalence

Population Partial Order


In a population of 10 people, let \(R \) be the "older than" relation and \(T \) be the "taller than" relation.

  1. Which of the following properties guarantee that \(R \) will be a linear order?

    Exercise 1

  2. Assume both \(R \) and \(T \) are linear orders. Which properties are guaranteed to be true for the product relation \(R \times T \)?

    Exercise 2

    Not symmetric because two distinct people cannot both be older and taller than each other.

    Not reflexive because a person cannot be older/taller than himself.

    Not linear because if person \(A \) is older than person \(B \) but \(B \) is taller than \(A \), then \(A\) and \(B\) are incomparable.