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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a direct proof?
💡 Hint: Consider its definition in the context of implications.
Question 2
Easy
Provide an example of a universally quantified statement.
💡 Hint: Think about properties of even and odd numbers.
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 does a direct proof do?
- Assumes Q is true
- Assumes P is true
- Has no assumptions
💡 Hint: Think about how direct proofs relate to implications.
Question 2
Is proof by contrapositive valid for proving implications?
- True
- False
💡 Hint: Recall the connection between a statement and its contrapositive.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the statement 'If n is a multiple of 4, then n² is a multiple of 16', prove it using a direct proof.
💡 Hint: Start by expressing n in terms of k.
Question 2
Prove 'if the product of two integers is odd, then both integers must be odd' using proof by contrapositive.
💡 Hint: Identify how even and odd integers interact when multiplied.
Challenge and get performance evaluation