Practice Mathematical Reasoning (2.1) - Fundamentals 47 - Discrete Mathematics

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9 questions

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6 sample questions

Question 1.
What is a proof in mathematics?
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Consider how you validate a statement mathematically.
Question 2.
Define Mathematical Reasoning.
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Think about why reasoning is essential in logic.
3Question 3.
What is mathematical reasoning primarily concerned with?
- Constructing random algorithms
- Deriving logical conclusions
- Speeding up code
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Think about how mathematicians ensure their statements hold true.
4Question 4.
A proof by contradiction assumes what?
- True
- False
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This type of proof is named for what it aims to expose.
Question 5.
Prove by induction that for all integers n ≥ 1, the sum of the first n even numbers equals n(n + 1).
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Set up your base case carefully, and then demonstrate the inductive step.
Question 6.
Demonstrate how mathematical reasoning is crucial in validating an algorithm's performance.
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Consider time complexity notation and proofs of correctness.

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