Practice Introduction To Cardinality (7.1) - Cantor's Theorem - Discrete Mathematics - Vol 2

Practice: Introduction to Cardinality

Lesson 7.1Cantor's Theorem

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8 questions

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6 sample questions

Question 1.
What does cardinality refer to?
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Think about how we count elements in a bag.
Question 2.
If set A has 3 elements, how many elements are in its power set?
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Remember the formula for the power set.
3Question 3.
What is the cardinality relationship established by Cantor's theorem?
- The cardinality of set A is greater than the power set P(A)
- The cardinality of set A is less than the power set P(A)
- The cardinality of set A is equal to the power set P(A)
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Remember the definition of the power set.
4Question 4.
True or False: The power set of a finite set always contains 2^n elements, where n is the number of elements in that set.
- True
- False
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Think about the counting of subsets.
Question 5.
Construct an example of a finite set and calculate its power set, then identify its cardinality.
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List all possible subsets to ensure you haven't missed any.
Question 6.
Explain the significance of Cantor's proof on the concept of different sizes of infinity. Provide a real-world analogy.
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Consider how different types of numbers can fill up the number line.

4 more questions in this section. Enroll free to practise them all.