Practice - Proof Strategies-II
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.
Practice Questions
Test your understanding with targeted questions
Provide a counterexample for the universal statement: 'All integers are positive.'
💡 Hint: Remember an integer can be negative.
What does WLOG mean?
💡 Hint: Think about simplifying cases in symmetrical arguments.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is a counterexample used for?
💡 Hint: Think about proving versus disproving.
True or False: A constructive proof provides no examples.
💡 Hint: Recall what you understood about constructive proofs.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Consider the statement: 'If a number is positive, then its square is positive.' Use a proof by cases to discuss how one would validate this without explicit value examples.
💡 Hint: Explore both positive and negative possibilities in numeric realms.
Demonstrate the non-constructive nature of proving that there are irrational numbers x and y such that xy is rational by using logical reasoning without establishing specific witnesses.
💡 Hint: One valid path through exponentiation fulfilling conditions is your aim.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.