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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a direct proof?
💡 Hint: Think about straightforward logical connections.
Question 2
Easy
What does it mean when we say a proof is vacuous?
💡 Hint: Check the definition of vacuous.
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 is true about a direct proof?
- It assumes the conclusion is false
- It shows the premise leading to the conclusion
- It uses indirect reasoning
💡 Hint: Remember, direct proofs follow a straightforward logical path.
Question 2
True or False: A vacuous proof can be used when the premise is true.
- True
- False
💡 Hint: Reflect on the conditions required for a vacuous proof.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove using contradiction: If n is an odd integer, then n^2 must also be odd.
💡 Hint: Focus on the implications of the assumption.
Question 2
Show that no positive integer squared can result in 2; use proof by contradiction.
💡 Hint: Explore the properties of rational numbers and their divisibility.
Challenge and get performance evaluation