Practice Equivalence Of Regular And Strong Induction (12.2.10)

Practise this section

9 questions

Flashcard drill
4 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define proof by induction in your own words.
Show hintHide hint
Think about how it serves as a mechanism to establish truth across an infinite set.
Question 2.
What must be shown in the base case of an induction proof?
Show hintHide hint
Consider the first number in the sequence you're working with.
3Question 3.
What is the first step in proof by induction?
- Establish the base case
- Prove k + 1
- Assume P(k) is true
Show hintHide hint
Remember, without a strong foundation, the rest doesn't stand.
4Question 4.
In strong induction, which series of assumptions can you use?
- P(k)
- P(b) through P(k)
- None
Show hintHide hint
Think about how many cases are at your disposal!
Question 5.
Prove that for any integer n ≥ 1, n^3 - n is divisible by 6.
Show hintHide hint
Focus on how n^3 and n can be restructured in forms conducive to divisibility.
Question 6.
Using strong induction, prove that any integer n ≥ 12 can be expressed as a sum of 4s and 5s.
Show hintHide hint
Consider how the addition of either a 4 or 5 affects the total in constructing k + 1.

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