Practice Tutorial 5 (9.1) - Tutorial 5 - Discrete Mathematics - Vol 2
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Tutorial 5

Practice - Tutorial 5

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is cardinality?

💡 Hint: Think about how we count items.

Question 2 Easy

Give an example of a countably infinite set.

💡 Hint: Can you list numbers sequentially starting from one?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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

💡 Hint: Recall if injective mapping implies equality in size of sets.

Question 2

Is the intersection of two uncountable sets always uncountable?

True
False

💡 Hint: Consider the examples of different types of sets.

Get performance evaluation

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove that the union of a countably infinite number of countable sets remains countable.

💡 Hint: Focus on how indices can dictate ordering.

Challenge 2 Hard

Given two uncountable sets, describe how their intersection can ever be countable.

💡 Hint: Assess the boundaries set by each uniqueness.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.