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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the base case in proof by induction?
💡 Hint: Think about where we start in proving our statement.
Question 2
Easy
State the two main components of proof by induction.
💡 Hint: Both terms start with the letter 'b' and 'i'.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What are the two main components of proof by induction?
- Inductive case and base case
- Base case and inductive step
- Base case and conclusion
💡 Hint: Both terms depict the foundational aspects of a proof.
Question 2
True or False: Strong induction assumes only the property for k to prove k+1.
- True
- False
💡 Hint: Reflect on what 'strong' means in this context.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove by induction that for all n >= 1, the sum of the first n even numbers is n(n + 1).
💡 Hint: Use the formula for the sum of the first k even numbers.
Question 2
Use strong induction to prove that every positive integer greater than 1 is either prime or can be factored into primes.
💡 Hint: Examine the factors of k + 1 in relation to those below it.
Challenge and get performance evaluation