Practice Definition Of Subsequences (18.1.2) - Subsequence Existence - Discrete Mathematics

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6 sample questions

Question 1.
Define 'subsequence' in your own words.
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Think about how you might pick numbers from a list without changing their order.
Question 2.
Give an example of a strictly increasing sequence.
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All the numbers must get bigger as you move along!
3Question 3.
What is a subsequence?
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Think about how you can rearrange numbers while keeping some of them in order.
4Question 4.
True or False: Every sequence of n distinct numbers contains a strictly increasing subsequence of length n.
- True
- False
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Consider what happens in sequences with positive and negative numbers.
Question 5.
Given the sequence of numbers 10, 20, 15, 25, 30, 5, find a subsequence that is strictly increasing.
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Look for numbers that ascend without backtracking.
Question 6.
You have a sequence with elements randomly ordered. How would you apply the pigeonhole principle to demonstrate the existence of either an increasing or decreasing subsequence?
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Make a table categorizing your sequences and their potential lengths.

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