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3 cards from this section. Quick, good the night before a test.
Define a poset.
Recall the three properties of the relation.
What does it mean for an element to cover another?
Think about visualizing it in a Hasse diagram.
What defines a partially ordered set (poset)?
Think of the definition of a poset.
True or False: Every maximal element must also be a cover.
Consider the definitions carefully.
Create a poset using the elements {A, B, C, D} such that you have at least two covers for one of the elements. Identify the covers and explain your structure.
Consider how you can relate elements while keeping some independent.
In a poset where X < Y and X < Z, if Y and Z are not related, identify the maximal elements. Then, determine if there can be a unique least element in this poset.
Visualize a scenario where you can see independent relationships.
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