Practice Construction Of The Subset S (7.3) - Cantor's Theorem - Discrete Mathematics - Vol 2

Practice: Construction of the Subset S

Lesson 7.3Cantor's Theorem

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9 questions

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6 sample questions

Question 1.
What is the power set of the set {a, b}?
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List all possible subsets.
Question 2.
Is the cardinality of {1, 2} greater than, less than, or equal to its power set?
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Consider how many subsets there are.
3Question 3.
What does Cantor's theorem state about the cardinality of a set and its power set?
- They are equal
- Power set is greater
- Power set is lesser
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Reflect on the relationship between a set and all of its subsets.
4Question 4.
Is the following statement true or false? 'The power set of a finite set is also finite.'
- True
- False
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Consider the formula for the size of the power set.
Question 5.
Prove using Cantor's theorem that the set of real numbers cannot be put into one-to-one correspondence with the natural numbers.
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Think about how you would apply the diagonal method to generate a new number.
Question 6.
Consider a set B. If the cardinality of B is 5, determine the cardinality of P(B) and describe what this means in terms of Cantor's theorem.
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Use the exponential relationship between set size and power sets.

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