Practice Tutorial 5 (9.1) - Tutorial 5 - 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 cardinality?
Show hintHide hint
Think about how we count items.
Question 2.
Give an example of a countably infinite set.
Show hintHide hint
Can you list numbers sequentially starting from one?
3Question 3.
What does the Schröder-Bernstein theorem establish?
- That every set has the same cardinality
- That two sets have the same cardinality if both have injective mappings
- That uncountable sets cannot be defined
Show hintHide hint
Recall if injective mapping implies equality in size of sets.
4Question 4.
Is the intersection of two uncountable sets always uncountable?
- True
- False
Show hintHide hint
Consider the examples of different types of sets.
Question 5.
Prove that the union of a countably infinite number of countable sets remains countable.
Show hintHide hint
Focus on how indices can dictate ordering.
Question 6.
Given two uncountable sets, describe how their intersection can ever be countable.
Show hintHide hint
Assess the boundaries set by each uniqueness.

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