Practice Base Case And Inductive Hypothesis (14.2.1) - Lecture -14 - 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 the smallest natural number applicable.
Question 2.
What does the inductive hypothesis assume?
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Consider what you need to prove next.
3Question 3.
What is the first step in proof by induction?
- Establishing the base case
- Formulating the hypothesis
- Proving for k + 1
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Think about where you start before building upon your argument.
4Question 4.
True or False: The inductive hypothesis is the part of the proof where we assume the statement is true for k.
- True
- False
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Consider what is required to build upon your assumption.
Question 5.
Prove that the formula for the sum of the first n odd numbers is n^2 using induction.
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Focus on the algebraic manipulation of odd numbers.
Question 6.
Show that for any integer n >= 1, 2^n - 1 is divisible by n.
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Factorize and explore the properties of exponential numbers.

4 more questions in this section. Enroll free to practise them all.