Practice Union Of Sets S (9.5.3) - Tutorial 5 - Discrete Mathematics

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6 sample questions

Question 1.
What is the cardinality of the set of integers?
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Think about the natural numbers.
Question 2.
Is the set of all real numbers between 0 and 1 countably infinite?
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Consider Cantor's diagonal argument.
3Question 3.
What is the definition of a countable set?
- A set that has a finite number of elements.
- A set that can be listed in correspondence with natural numbers.
- Any set.
- An infinite set.
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Think about how we can list elements of a set.
4Question 4.
True or False: The intersection of two uncountable sets is always uncountable.
- True
- False
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Consider overlapping intervals.
Question 5.
Given two infinite sets, A and B, with A included in B, prove A's cardinality is less than or equal to B.
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Start by demonstrating elements of A can map to B.
Question 6.
Construct a sequence in which the union of subsets remains countable. Provide an example.
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List down individual subsets and combine interestingly.

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