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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Give a counterexample for the statement 'All integers are positive.'
💡 Hint: Think of integers that are less than zero.
Question 2
Easy
What does WLOG stand for?
💡 Hint: It allows you to simplify your proof.
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 proof by cases?
- A single example
- Breaking down a statement
- A generalization
💡 Hint: Think about how we validate universal statements.
Question 2
True or False: A counterexample can prove a universally quantified statement is true.
- True
- False
💡 Hint: Remember what a counterexample represents.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that for any integer n, if n is odd, then n² is also odd using proof by cases.
💡 Hint: Break down what odd means in terms of definition.
Question 2
Discuss the implications of constructing a non-constructive proof regarding irrationality and rationality.
💡 Hint: Explore examples like √2 raised to itself.
Challenge and get performance evaluation