Practice Direct Proof Method (10.1.2) - Proof Strategies-I - Discrete Mathematics - Vol 1
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Direct Proof Method

Practice - Direct Proof Method

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is a direct proof?

💡 Hint: Think about how you can show something true by assuming its starting conditions.

Question 2 Easy

Give an example of a vacuous proof.

💡 Hint: Remember when is an implication automatically considered true.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What method allows proving P → Q through ¬Q → ¬P?

Indirect proof
Direct proof
Vacuous proof

💡 Hint: Look at how the implications relate logically.

Question 2

True or False: A vacuous proof is always true?

True
False

💡 Hint: Remember the condition under which this holds.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Provide a proof by contradiction that demonstrates the irrationality of √3.

💡 Hint: Focus on deducing properties of squares and their implications on parity.

Challenge 2 Hard

Create an example of application where a vacuous proof is used correctly in a complex mathematical theorem.

💡 Hint: Think of statements that hinge on conditions not being satisfied.

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Reference links

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