Practice Part (b): Counting Bijective Functions (2.4.3)

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6 sample questions

Question 1.
Define a bijection in your own words.
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Think about injective and surjective functions.
Question 2.
Is the function f: {1, 2, 3} → {4, 4, 4} a surjection?
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Check if every element in the codomain has a pre-image.
3Question 3.
What is a bijective function?
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Consider the definitions of injective and surjective functions.
4Question 4.
True or False: All surjective functions are bijective functions.
- True
- False
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Think about the relationship between injectivity and surjectivity.
Question 5.
Given two infinite sets A and B, describe a surjective function that is not bijective.
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Use different relationships for mappings that overlap.
Question 6.
How would you prove that every bijective function has an inverse? Discuss the relationship.
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Focus on the uniqueness of mappings and how they allow reversibility.

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