Practice Conclusion On Divisibility (18.3.3) - Subsequence Existence - Discrete Mathematics - Vol 2

Practice: Conclusion on Divisibility

Lesson 18.3.3Subsequence Existence

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8 questions

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6 sample questions

Question 1.
Define a strictly increasing sequence. Give an example.
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Think about numbers that follow one another and keep getting larger.
Question 2.
What is a subsequence?
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Remember, the order should remain the same.
3Question 3.
What defines a strictly increasing sequence?
- Each number is greater than the last
- Each number is less than the last
- Numbers can repeat
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Think about how numbers compare to each other.
4Question 4.
True or False: In every set of n + 1 distinct real numbers, there must be a strictly increasing subsequence of length n + 1.
- True
- False
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Reflect on the properties of increasing subsequences.
Question 5.
Using 9 distinct integers from 1 to 20, demonstrate through a sequence how the pigeonhole principle ensures either an increasing or decreasing subsequence of length 5.
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Look for how many distinct lengths can be achieved and overlap them.
Question 6.
Given the sequence of prime numbers up to 30, find a subsequence of at least 4 numbers that is strictly increasing and explain your reasoning.
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Remember that primes inherently don't repeat, aiding your subsequence choice.

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