Practice Introduction (2.1.1) - Introduction - Discrete Mathematics

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6 sample questions

Question 1.
Define a surjective function in your own words.
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Think about the elements in both sets and how they relate.
Question 2.
What is S(n, k) in terms of Stirling numbers?
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Consider the connection to set partitions.
3Question 3.
What is a surjective function?
- A function where every element in the domain is unique.
- A function where every codomain element has at least one pre-image.
- A function that is always linear.
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Think about the relationship between the domain and codomain elements.
4Question 4.
Is a bijective function always injective?
- True
- False
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Recall the definitions of injective and bijective functions.
Question 5.
Given a set of size 5, how many different surjective functions can be created to a set of size 3?
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Remember to break it down into partitions and mappings.
Question 6.
Prove that there exists a surjective function that is not injective by constructing a specific example.
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Focus on the mappings from domain to codomain.

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