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3 cards from this section. Quick, good the night before a test.
What does reflexive mean in partial ordering?
Think about how words relate to themselves.
Is the divides relationship a total order?
Consider if every number can be divided by another.
What property indicates that each element relates to itself?
Think about how a word relates to itself in a dictionary.
True or False: In partial ordering, every element must relate to every other element.
Consider the divides relationship example.
Consider a set of integers from 1 to 10 and define a partial order through multiplicative divisibility. Discuss whether this forms a poset.
Check each property against the definition of poset.
Construct a Hasse diagram for the set {1, 2, 3, 4, 6, 12} under the divides relation.
Remember to remove unnecessary connections.
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