Practice - Part (a): Counting Functions
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Practice Questions
Test your understanding with targeted questions
Define an injective function and give an example.
💡 Hint: Think of a simple linear function.
What is a surjective function?
💡 Hint: Consider mappings to fewer elements.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What defines a surjective function?
💡 Hint: Think of it as 'onto' mapping.
If a function has 5 elements in the domain and 3 in the codomain, how many injective functions can it have?
💡 Hint: Consider if you can assign unique outputs for all inputs.
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Challenge Problems
Push your limits with advanced challenges
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.
💡 Hint: Reflect on the definitions of injective versus surjective.
Calculate the number of surjective functions from set A with 5 elements to set B with 3 elements using Stirling numbers.
💡 Hint: Use the Stirling function properties and recall how permutations affect partitions.
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