Practice Listing Of Set S (9.4.2) - Tutorial 5 - Discrete Mathematics

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6 sample questions

Question 1.
What is the definition of cardinality?
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Think about how we can count elements in a group.
Question 2.
Give an example of an injective mapping.
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Consider functions that don’t pair different elements together.
3Question 3.
What theorem states that two sets have the same cardinality when there are injective mappings both ways?
- Cantor's Theorem
- Schroder-Bernstein Theorem
- Euler's Theorem
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Recall the theorem focused on injective mappings.
4Question 4.
True or False: There exists a countably infinite subset in every infinite set.
- True
- False
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Think about the properties of sets with infinite particles.
Question 5.
Using the mapping concept, prove that both (0, 1) and (0, 1] have the same cardinality systematically.
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Consider visual aids for the mappings.
Question 6.
Construct two uncountable sets with finite intersection. Explore their properties.
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Use boundaries of sets for example constructions.

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