Practice Discrete Mathematics (2) - Introduction - Discrete Mathematics

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6 sample questions

Question 1.
Define a surjective function.
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Think of it as every 'output' must have at least one 'input'.
Question 2.
What is an injective function?
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Does every unique input need to yield a unique output?
3Question 3.
What defines a surjective function?
- Each element in the codomain has at least one corresponding pre-image.
- No two inputs map to the same output.
- Both A and B.
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Focus on what needs to be covered in terms of outputs.
4Question 4.
True or False: Every bijective function is also surjective.
- True
- False
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Consider the definitions of the terms involved.
Question 5.
Construct a surjective function from the set {1, 2, 3, 4} to {A, B} and describe its properties.
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Keep in mind the requirements for surjectiveness.
Question 6.
Provide a proof using induction that the number of bijective functions from a set of size n to itself is n!.
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Use the principle of mathematical induction to structure your proof.

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