Practice Proof By Contraposition (10.1.3.1) - Proof Strategies-I - Discrete Mathematics - Vol 1
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

Proof by Contraposition

Practice - Proof by Contraposition

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 proof by contraposition?

💡 Hint: Think about the relationship between P and Q.

Question 2 Easy

If P → Q is true, what can we say about ¬P?

💡 Hint: Focus on the logic of implications.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does proof by contraposition allow us to do?

Prove P directly
Prove ¬Q leads to ¬P
Confirm P is always true

💡 Hint: Focus on the structure of the implication.

Question 2

True or False: Vacuous proofs are always useful.

True
False

💡 Hint: Consider when a premise may easily be false.

Get performance evaluation

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove by contradiction that √3 is irrational.

💡 Hint: Think about the implications of squaring both sides.

Challenge 2 Hard

Demonstrate using vacuous proof that 'If n > 5, then n^2 > 25' holds true when n = 3.

💡 Hint: Evaluate the initial premise.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.