Practice Subsets Of Countable Sets (4.3.3) - Module No # 05 - Discrete Mathematics

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6 sample questions

Question 1.
What makes a set countable?
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Think about natural numbers.
Question 2.
Is the set of all integers countable?
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How do we list numbers?
3Question 3.
Which of the following sets is countable?
- The set of all real numbers
- The set of all integers
- The set of all points in a plane
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Think about whether you can list these numbers.
4Question 4.
True or False: A union of two countable sets is also countable.
- True
- False
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Reflect on combining two lists.
Question 5.
Explain the process of proving that the Cartesian product ℤ x ℤ is countable. Detail each step involved.
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Visualize the spiral; how would you traverse the plane?
Question 6.
Demonstrate how to prove two countable sets A and B have the same cardinality through the use of the Schroder-Bernstein theorem.
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Map elements carefully; consider which sets you could use.

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