Practice Base Case And Inductive Hypothesis (14.2.1) - Lecture -14 - Discrete Mathematics - Vol 1
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Base Case and Inductive Hypothesis

Practice - Base Case and Inductive Hypothesis

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Practice Questions

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Question 1 Easy

What is the base case in proof by induction?

💡 Hint: Think about the smallest natural number applicable.

Question 2 Easy

What does the inductive hypothesis assume?

💡 Hint: Consider what you need to prove next.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the first step in proof by induction?

Establishing the base case
Formulating the hypothesis
Proving for k + 1

💡 Hint: Think about where you start before building upon your argument.

Question 2

True or False: The inductive hypothesis is the part of the proof where we assume the statement is true for k.

True
False

💡 Hint: Consider what is required to build upon your assumption.

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Challenge Problems

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Challenge 1 Hard

Prove that the formula for the sum of the first n odd numbers is n^2 using induction.

💡 Hint: Focus on the algebraic manipulation of odd numbers.

Challenge 2 Hard

Show that for any integer n >= 1, 2^n - 1 is divisible by n.

💡 Hint: Factorize and explore the properties of exponential numbers.

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