Practice - Proof by Cases
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Practice Questions
Test your understanding with targeted questions
Give a counterexample for the statement 'All integers are positive.'
💡 Hint: Think of integers that are less than zero.
What does WLOG stand for?
💡 Hint: It allows you to simplify your proof.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is proof by cases?
💡 Hint: Think about how we validate universal statements.
True or False: A counterexample can prove a universally quantified statement is true.
💡 Hint: Remember what a counterexample represents.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
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.
Discuss the implications of constructing a non-constructive proof regarding irrationality and rationality.
💡 Hint: Explore examples like √2 raised to itself.
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