Practice Example With Positive Integers (23.2.5) - Partial Ordering

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6 sample questions

Question 1.
What does reflexivity mean in a partial ordering?
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Think of how you would describe the relationship between a word and itself.
Question 2.
Provide an example of antisymmetry.
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Consider two integers and their divisibility.
3Question 3.
What is one property of partial ordering?
- Reflexivity
- Addition
- Multiplication
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Consider the relationship between an element and itself.
4Question 4.
True or False: In a total ordering, some elements can be incomparable.
- True
- False
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Think about the definition of total ordering.
Question 5.
Consider a set of numbers {2, 4, 8, 16}. Define the divides relation and create a Hasse diagram.
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Start from the smallest factor and build upwards.
Question 6.
Given the set of subsets S = {A, B, C}, define the subset relation and demonstrate its partial ordering.
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Include all possible combinations and conversely related pairs.

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