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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Provide a counterexample for the universal statement: 'All integers are positive.'
💡 Hint: Remember an integer can be negative.
Question 2
Easy
What does WLOG mean?
💡 Hint: Think about simplifying cases in symmetrical arguments.
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 a counterexample used for?
- To prove a statement true
- To disprove a statement
- To illustrate a property
💡 Hint: Think about proving versus disproving.
Question 2
True or False: A constructive proof provides no examples.
- True
- False
💡 Hint: Recall what you understood about constructive proofs.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation