Practice Base Case And Inductive Step (12.2.4) - Induction - Discrete Mathematics

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6 sample questions

Question 1.
What is the base case in proof by induction?
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Think about where we start in proving our statement.
Question 2.
State the two main components of proof by induction.
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Both terms start with the letter 'b' and 'i'.
3Question 3.
What are the two main components of proof by induction?
- Inductive case and base case
- Base case and inductive step
- Base case and conclusion
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Both terms depict the foundational aspects of a proof.
4Question 4.
True or False: Strong induction assumes only the property for k to prove k+1.
- True
- False
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Reflect on what 'strong' means in this context.
Question 5.
Prove by induction that for all n >= 1, the sum of the first n even numbers is n(n + 1).
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Use the formula for the sum of the first k even numbers.
Question 6.
Use strong induction to prove that every positive integer greater than 1 is either prime or can be factored into primes.
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Examine the factors of k + 1 in relation to those below it.

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