Practice Cantor's Theorem (7) - Cantor's Theorem - Discrete Mathematics

Practise this section

8 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is the power set of A = {a, b}?
Show hintHide hint
Remember, the power set includes all subsets.
Question 2.
Define cardinality.
Show hintHide hint
Think about how to measure the size of a set.
3Question 3.
What is the relationship between a set and its power set according to Cantor's Theorem?
- The sizes are equal
- The power set is larger
- The power set is smaller
Show hintHide hint
Think about how many subsets can be formed.
4Question 4.
True or False: A power set of a finite set always has a finite number of elements.
- True
- False
Show hintHide hint
Consider the formula for power sets.
Question 5.
Construct a set A with 4 elements and illustrate the power set P(A). Explain the relationship of sizes.
Show hintHide hint
Count the number of subsets and relate it back to the power set definition.
Question 6.
Explain how Cantor's diagonalization argument not only proves the non-existence of a surjective function but also illustrates the concept of uncountability.
Show hintHide hint
Reflect on the steps in constructing the diagonal set.

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