Practice Types Of Functions (2.2) - Relations and Functions

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6 sample questions

Question 1.
Define an injective function.
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Think about how inputs are related to outputs.
Question 2.
What is the range of this function: f: {1, 2, 3} → {a, b} where f(1)=a, f(2)=b, f(3)=b?
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Look for the outputs produced from the inputs.
3Question 3.
What is an injective function?
- A function with identical outputs for different inputs.
- A function where every input has a unique output.
- A function that maps all domain elements to at least one output.
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Focus on the uniqueness of mapping.
4Question 4.
Is a function f: {1, 2} → {a, b} with f(1)=a and f(2)=b both injective and surjective?
- True
- False
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Check both properties for verification.
Question 5.
Given two sets A = {1, 2, 3} and B = {a, b, c, d}, can we have a surjective function defined from A to B? Justify your answer.
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Think about the number of outputs compared to inputs.
Question 6.
Construct an example of a function f: {1, 2, 3} → {x, y} that is injective but not surjective. Explain your choice.
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Make sure to check for any repeated outputs when creating your function.

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