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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a counterexample?
💡 Hint: Think of an example that disproves a general claim.
Question 2
Easy
Explain proof by cases in one sentence.
💡 Hint: No hint provided
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?
- An example that proves a statement true
- An example that disproves a statement
- An irrelevant example
💡 Hint: Think of examples that are the opposite of what the statement claims.
Question 2
Using w.l.o.g. means choosing a particular case that constrains the proof.
- True
- False
💡 Hint: Consider how this simplifies your reasoning.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Using w.l.o.g., prove that for any two real numbers x and y, if x + y is odd, one of them must be even.
💡 Hint: Explore the definitions of odd and even carefully.
Question 2
Show that the product of any two odd integers is odd.
💡 Hint: Factor out to see the result!
Challenge and get performance evaluation