Practice Summary Of Proof Methods (10.2.1) - Proof Strategies-I - Discrete Mathematics - Vol 1
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Summary of Proof Methods

Practice - Summary of Proof Methods

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Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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