Partially Ordered Sets · Operations on Partially Ordered Sets

Lesson 2

Nikolai Chukhin · Alexander S. Kulikov

A product order is the order on the set \(X \times Y\), defined as: \((x_{1}, y_{1}) \preceq (x_{2}, y_{2})\) if \(x_{1} \preceq_{X} x_{2}\) and \(y_{1} \preceq_{Y} y_{2}\).

Problem. Let the orders \((X, \preceq_{X})\) and \((Y, \preceq_{Y})\) be linear. Is the product order linear?

5 points

  1. Yes, it will always be linear.

  2. No, it will not necessarily be linear.