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

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6 sample questions

Question 1.
What is a direct proof?
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Think about how you can show something true by assuming its starting conditions.
Question 2.
Give an example of a vacuous proof.
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Remember when is an implication automatically considered true.
3Question 3.
What method allows proving P → Q through ¬Q → ¬P?
- Indirect proof
- Direct proof
- Vacuous proof
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Look at how the implications relate logically.
4Question 4.
True or False: A vacuous proof is always true?
- True
- False
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Remember the condition under which this holds.
Question 5.
Provide a proof by contradiction that demonstrates the irrationality of √3.
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Focus on deducing properties of squares and their implications on parity.
Question 6.
Create an example of application where a vacuous proof is used correctly in a complex mathematical theorem.
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Think of statements that hinge on conditions not being satisfied.

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