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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does it mean to prove something by contradiction?
💡 Hint: Think about negation!
Question 2
Easy
Is the statement 'If 5 is even, then 10 is greater than 5' vacuously true?
💡 Hint: Focus on the truth value of the premise.
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 the main purpose of proof by contradiction?
💡 Hint: Remember the process of negation leading to invalidity.
Question 2
True or False: Proof by contrapositive shows that p → q is equivalent to ¬q → ¬p.
💡 Hint: Think about logical statements.
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^2 is odd, then n must be odd using contradiction.
💡 Hint: Use the properties of even and odd integers.
Question 2
Show that if n is a natural number such that n^2 < n, then n must be 1.
💡 Hint: Consider properties of inequalities with natural numbers.
Challenge and get performance evaluation