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Practice Questions
Test your understanding with targeted questions related to the topic.
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.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
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.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove by contradiction that √3 is irrational.
💡 Hint: Think about the implications of squaring both sides.
Question 2
Demonstrate using vacuous proof that 'If n > 5, then n^2 > 25' holds true when n = 3.
💡 Hint: Evaluate the initial premise.
Challenge and get performance evaluation