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3 cards from this section. Quick, good the night before a test.
What does it mean for one element to cover another in a poset?
Think about how we represent relationships graphically.
Can a poset have multiple maximal elements?
Consider how elements relate to each other without having upper boundaries.
What is a maximal element in a poset?
Think about what it means to have no elements above.
True or False: Every poset has a least element.
Consider the conditions under which elements exist.
Given a set of elements {A, B, C, D, E} with the following relations: A < B, A < C, B < D, C < D, D < E. Identify all maximal and minimal elements, and justify your reasoning.
Visualize the elements using a Hasse diagram for clarity.
Construct a Hasse diagram for the set {1, 2, 3, 4} with relations including 1 < 2, 1 < 3, 2 < 4, and 3 < 4. Identify each type of element.
Sketch carefully and check the connections.
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