Practice Part (a): Counting Functions (2.4.1) - Introduction - Discrete Mathematics

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6 sample questions

Question 1.
Define an injective function and give an example.
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Think of a simple linear function.
Question 2.
What is a surjective function?
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Consider mappings to fewer elements.
3Question 3.
What defines a surjective function?
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Think of it as 'onto' mapping.
4Question 4.
If a function has 5 elements in the domain and 3 in the codomain, how many injective functions can it have?
- 1
- 0
- 6
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Consider if you can assign unique outputs for all inputs.
Question 5.
Prove that if you're given a surjective function from a finite set A (with 4 elements) to another finite set B (with 3 elements), A cannot contain an injective function.
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Reflect on the definitions of injective versus surjective.
Question 6.
Calculate the number of surjective functions from set A with 5 elements to set B with 3 elements using Stirling numbers.
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Use the Stirling function properties and recall how permutations affect partitions.

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