Practice Conclusion (10.2) - 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 straightforward logical connections.
Question 2.
What does it mean when we say a proof is vacuous?
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Check the definition of vacuous.
3Question 3.
What is true about a direct proof?
- It assumes the conclusion is false
- It shows the premise leading to the conclusion
- It uses indirect reasoning
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Remember, direct proofs follow a straightforward logical path.
4Question 4.
True or False: A vacuous proof can be used when the premise is true.
- True
- False
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Reflect on the conditions required for a vacuous proof.
Question 5.
Prove using contradiction: If n is an odd integer, then n^2 must also be odd.
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Focus on the implications of the assumption.
Question 6.
Show that no positive integer squared can result in 2; use proof by contradiction.
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Explore the properties of rational numbers and their divisibility.

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