Practice Proof By Induction (14.2) - Lecture -14 - Discrete Mathematics

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6 sample questions

Question 1.
What are the two main steps in a proof by induction?
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Think about the first step in proving something is true.
Question 2.
What is the base case for proving that the arithmetic mean is at least the geometric mean for 2 numbers?
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Consider two positive integers and their means.
3Question 3.
What is the purpose of the base case in proof by induction?
- To prove the statement for all integers
- To establish the truth for one initial case
- To derive a general formula
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Remember that every proof needs a starting point to build upon.
4Question 4.
A celebrity in a party knows everyone but is not known by anyone.
- True
- False
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Think about the social dynamics of knowing someone.
Question 5.
Prove using induction that for every n > 1, n! > 2^n.
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Consider how quickly factorial values grow compared to powers!
Question 6.
Prove that for any integer n, n² + n is even.
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Factor to see the evenness clearly.

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