Practice Examples Of Countably Infinite Sets (4.1.2) - Module No # 05 - 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 defines a countably infinite set?
Show hintHide hint
Think about how you could make a pairing with the number line.
Question 2.
How many rational numbers are between 1 and 2?
Show hintHide hint
Consider how you can divide 1 and 2 into different fractions.
3Question 3.
Is the set of rational numbers countable?
- True
- False
Show hintHide hint
Think about how you could list fractions systematically.
4Question 4.
What is the term for a set that can be put into a one-to-one correspondence with positive integers?
- Countable
- Finite
- Uncountable
Show hintHide hint
Consider how you might measure the size of a set.
Question 5.
Prove that the union of countably infinite sets A and B is also countable.
Show hintHide hint
What would happen if you outlined one set's items and then went through the other?
Question 6.
How can you demonstrate that any subset of a countably infinite set is either finite or countably infinite?
Show hintHide hint
Consider how a small class can still join together with a larger class!

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