Consider the Poset with the Following Hasse Diagram

question 6

Essay

Consider the poset with the following Hasse diagram.
(a) Find all maximal elements of the poset.
(b) Find all minimal elements of the poset.
(c) Find the least element of the poset if it exists, or show that it does not exist.
(d) Find the greatest element of the poset if it exists, or show that it does not exist.
(e) What is the greatest lower bound of the set {a, b, c}?
(f) What is the least upper bound of the set {a, b, c}?

---

Definitions:

1930s

A decade characterized by the Great Depression, which had a profound impact on the world economy, social conditions, and the political landscape.

John Collier

An American social reformer and advocate for the rights of Native Americans, serving as Commissioner for the Bureau of Indian Affairs from 1933 to 1945, where he promoted policies to preserve Native American culture and autonomy.

Bureau of Indian Affairs

A federal agency within the United States tasked with the administration and management of lands and resources for Native American tribes.

Social Worker

A professional dedicated to helping individuals, families, and communities to cope with challenges and improve their well-being.