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}?

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Definitions:

Physical Heights

A measurement indicating the vertical dimension or elevation of an object or a person.

Predictive Validity

The extent to which a score on a scale or test predicts future performance on a related task or outcome.

Computer Programming Aptitude Test

A standardized test designed to assess an individual's potential to succeed in and understand computer programming and related disciplines.

Content Validity

The extent to which a test measures all aspects of the concept or construct it intends to measure.