Practice Unique Factorization (18.3.1) - Subsequence Existence - Discrete Mathematics - Vol 2

Practice: Unique Factorization

Lesson 18.3.1Subsequence Existence

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9 questions

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2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define a subsequence.
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Think about examples of both sequences and subsequences.
Question 2.
Is the sequence [4, 3, 2, 1] strictly increasing or decreasing?
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Check the relationship between each consecutive term.
3Question 3.
What is a strictly increasing sequence?
- A sequence where each term is less than the following term
- A sequence where each term is greater than the previous term
- A sequence sorted in descending order
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Look out for terms relative to one another.
4Question 4.
True or False: Every sequence of n + 1 distinct real numbers contains a decreasing subsequence of length n + 1.
- True
- False
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Consider subsequences formed from increasing distinct numbers.
Question 5.
Given the sequence [9, 7, 5, 8, 10], demonstrate that there exists either a strictly increasing or decreasing subsequence.
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Look at the sequence order closely, not all need to be taken together.
Question 6.
Using a custom sequence of 7 distinct numbers, explain how you can derive an increasing subsequence of at least 5.
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Choose wisely to increase; several must be smaller than your larger picks.

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