Partially Ordered Sets · Hasse Diagrams

Lesson 3

Nikolai Chukhin · Alexander S. Kulikov

Problem. Consider the following poset \((X, \preceq)\): \(X\) is the set of positive divisors of 840 and \(x \preceq y\) if \(x \mid y\). Mark all true statements.

5 points

  1. \(\{6, 10, 24\}\) is an antichain

  2. \(\{840, 1, 60, 20\}\) is a chain

  3. \(\{24, 40, 56, 60, 84, 140, 210\}\) is an antichain

  4. \(\{1, 3, 6, 42, 84\}\) is a chain