Practice Divisibility In Arbitrary Subsets (18.3) - Subsequence Existence

Practice: Divisibility in Arbitrary Subsets

Lesson 18.3Subsequence Existence

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8 questions

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6 sample questions

Question 1.
Define a strictly increasing sequence.
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Think of numbers placed from smallest to largest.
Question 2.
What is a subsequence?
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Consider how you can pick elements but skip some.
3Question 3.
What defines a strictly decreasing sequence?
- All terms are equal
- Each term is less than the next
- Each term is greater than the next
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Visualize a staircase going down.
4Question 4.
True or False: A subsequence must consist of consecutive elements.
- True
- False
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Think about how you might skip numbers in a list.
Question 5.
Prove that in any sequence of 10 distinct positive integers, there exists a subsequence of length 4 that is either strictly increasing or strictly decreasing.
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Look for the lengths you can compare among backs and see how they lead to pairs.
Question 6.
Given a set of 15 random numbers, verify if the assertion that you can find a subsequence of length 5 that’s either increasing or decreasing holds true.
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Divide the numbers into groups based on parity and analyze their compositions.

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