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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: Think about what happens if P is true.
Question 2
Easy
If P is false, what can we say about P → Q?
💡 Hint: Consider the definition of implications.
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 direct proof?
- A method using contradiction
- A method where P leads directly to Q
- A method proving ¬P → Q
💡 Hint: Think about the simplest way to prove an implication.
Question 2
If P is false, what can we conclude about P → Q?
- True
- False
💡 Hint: Refer back to the definition of the implication.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that if a triangle has sides of lengths a, b, and c, and if a^2 + b^2 < c^2, then the triangle is not valid.
💡 Hint: Start by assuming the triangle is valid and proceed to demonstrate inconsistency.
Question 2
Demonstrate using proof by contrapositive that if an integer n is even, then n^2 is even.
💡 Hint: Work with definitions of odd and even integers to show results systematically.
Challenge and get performance evaluation